Holt Mcdougal Geometry Larson Boswell Kanold Stiff

Holt McDougal Geometry Larson Boswell Kanold Stiff

Practice Workbook The Practice Workbook provides additional practice for every lesson in the textbook. The workbook covers essential vocabulary, skills, and problem solving. Space is provided for students to show their work.

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ISBN 978-0-547-71004-4 XXX-X-XXX-XXXXX-X

1 2 3 4 5 6 7 8 9 10 XXX 20 19 18 17 16 15 14 13 12 11

4500000000 A B C D E F G Contents Chapter 1 Practice for Lessons 1.1–1.6 ...... 1–18 2 Practice for Lessons 2.1–2.7 ...... 19–39 3 Practice for Lessons 3.1–3.6 ...... 40–57 4 Practice for Lessons 4.1–4.9 ...... 58–84 5 Practice for Lessons 5.1–5.6 ...... 85–102 6 Practice for Lessons 6.1–6.6 ...... 103–120 7 Practice for Lessons 7.1–7.7 ...... 121–141 8 Practice for Lessons 8.1–8.6 ...... 142–159 9 Practice for Lessons 9.1–9.7 ...... 160–180 10 Practice for Lessons 10.1–10.7 ...... 181–201 11 Practice for Lessons 11.1–11.9 ...... 202–228

Geometry Practice Workbook iii

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. In Exercises13–15,usethediagram. Sketch theﬁguredescribed. Use thediagramtodecidewhethergivenstatementis Name 15. 14. 13. 11. 8. 3. 2. 1. 9. 7. 6. 5. 4. LESSON Two rays thatdonotintersect Theintersectionofplane Theintersectionofplane Theintersectionof Theintersectionof Allpointson Points Points Name3linesthatintersectatpoint Nameapairofoppositerays. Name12different rays. Threelinesthatintersectinthreepoints 1.1 EG # ——————————————————————— ## $ and H H For usewiththelesson“IdentifyPoints,Lines,andPlanes” Practice FG # , , ## I I $ , and , and areoppositerays. # GI ## $ J G

and arecoplanar. arecollinear. @ @ EF EF ## ## $ $ GF # , andplane

@ $ HI ## arecoplanar. EFI EGH $

, and 10. andplane and plane @ JG ## JKH $ C ispoint

. is 12. JKG @ HI JGI ## $

. G is ispoint . HG @ ## $ . A ray thatintersectsaplaneinonepoint Three planesthatintersectinoneline G .

AB E true E Date H or J C ———————————— false G K I . F D Practice Workbook Geometry 1 2 Name

segment Graph theinequalityonanumberline.Tell whetherthegraphisa determine whetherthepointisonline. You aregivenan equationofalineandpoint.Usesubstitutionto

26. 24. 21. 18. 17. 16. Practice Workbook Geometry LESSON

2 Sketch plane Draw fournoncollinearpoints

1.1 x x y plane ———————————————————————

x b r 5

2 0or 2 5 , a 25.

y x N

For usewiththelesson“IdentifyPoints,Lines,andPlanes” Practice 5 1 , butnotplane ray x

7; 3; r 8 or A A 27. M (3, (1, 8) intersectingplane rays 2 1) , a

M . point continued 22. 19. A , ora , B

N , x y . Then sketch plane C

1 5 , and line 6 2 y x

. 5

D 1 40; . Then sketch 3; A A

2 (6, 3) ( 2 | b 10, 5) x | O x

sothatitintersects b 0 AB } 5 , BC # ## 23. 20. $ , and

Date

2 y

5 AD @ x ———————————— ##

2 $ 2

. 4 3 y x

5 2 6; 2 14; A (2, 0) A ( 2 6, 2)

a. a.

29. 28. LESSON 1.1 b. b. using vanishing points. Perspective Drawings Counter Stools c. ——————————————————————— Redraw theprismsothatituses Usingheavy dashedlines,draw the Supposethateachstoolisplacedon occur. possibly be? Which ofthetwo stoolscouldthis side toonyour kitchenﬂoor. two vanishing points. hidden linesoftheprism. or why not. rock fromsidetoside? Do you expect eitherofthestoolsto thatisslightlya ﬂatsurface sloped. Does thedrawing attheright One stoolrocksslightly from Explain represent aperspective drawing? For usewiththelesson“IdentifyPoints,Lines,andPlanes” Practice why orwhy not. Two different typesofstoolsareshown below. Explain Recallfromthetext, thataperspective drawing isdrawn why thismight continued Explain

why Three-legged stool Date

———————————— Four-legged stool Practice Workbook Geometry

3 4

9. line segmentsnamedarecongruent. Plot thegivenpointsinacoordinateplane.Thendeterminewhether Use theSegmentAdditionPostulatetoﬁndindicatedlength. Measure thelengthofsegmenttonearesttenthacentimeter. Name 7. 4. 1. Practice Workbook Geometry LESSON

1.2 RT AB E A EG } AB } Find ——————————————————————— ( (2, 2), 2 and and 1 3, 4), RT y For usewiththelesson“UseSegmentsandCongruence” Practice 1 CD } 78.5 17 . B FH } 1 (4, 2), F

( y 2 1 1, 4), C S ( 2 G x x 1,

(2, 4), 2

1),

D H ( ( 5. 2. 2 2

1, 1); 1, 1); A MN Find C 8. 10. BC 25 . B 54

M R RS } MN } (3, 5), (1, and and 2 3) , TU } S OP }

3 (10, 5), 2

N y

y (4, 3 2 6. 3. Date

2 T M EF Find 3), ( 2 ———————————— x x 4, O MN N (3, 4), 2 3), . U P ( (4, 4); 2 32 11, 26 2 3); P

Find theindicatedlength. the indicatedlength. In thediagram,points Use thenumberlinetoﬁndindicateddistance. are collinear, 15. 11. 25. 24. 23. 22. 21. 20. 19. LESSON

1.2 ST RS CD CY BD AB CE AB CZ XC Find 2 ——————————————————————— 10 4

x 2 ST ABC DE 9 For usewiththelesson“UseSegmentsandCongruence” Practice . 2 8 AB 32 2

7 12 5

x 2 BC 6 16. 12. 2

A 5 5 ,

CX 2 B continued AE AD 4 ,

C, 5 2

26. 3

and YZ, AD 2

Find

2 A BC AB D 2 arecollinear, points 10123

AC 5 43 14 B 54, . 4 17. 13. x XY 1 C

5 BE CD x 22,and X 2

4 45

C Y 27. XZ , 6 X Date Find

D 5 , Z Y NP MN 33.Find x , and 2 ———————————— 18. 14. 5 NP

. DE BD Z

6 x 3 2 x Practice Workbook 23 1 2 Geometry 5 6 Name

equation intermsof Point 32. 30. 28. Practice Workbook Geometry LESSON

1.2 KH KH JK JK Hiking much farther doyou needtohikemuch farther toreachtheendoftrail? beginning ofthetrailandhike for90minutesatarateof1.4milesperhour. How HJ HJ ——————————————————————— 1 J

isbetween

5 5

5 5 Distance (mi) Ranger Station 5 5 A 1 8 3 (3, 2) 5 2 3 38 25 For usewiththelesson“UseSegmentsandCongruence” Practice x x Onthemap, x x

2 2

1 10 4 Rest Area H and x . Solvetheequation.Thenﬁnd AB } representsatrailthatyou arehiking. You fromthe start Distance (mi) K B continued on (8.2, 2) HK } .Usethegiveninformationtowritean

31. 29.

KH KH JK JK HJ HJ

5 5

5 5 5 5

3 5 x 5 22 HJ } 4 x

2 x

2 2 and 9 4 3 Date JK . ————————————

the otherendpoint Use thegivenendpoint given endpoints. Find thecoordinatesofmidpointsegmentwith 5. indicated length. In thediagram, 4. Name 12. 10. 14. 8. 3. 2. 1. LESSON

Point Point Line Line

1.3 LMN S R R H Find ——————————————————————— (4, ( (6, 0), ( 2 2 x 3, 2 5, 5)and LN

JK RS 1 C T 1) and 2 For usewiththelesson“UseMidpointandDistanceFormulas” Practice bisects bisects 94 bisects bisects M . 2), (0, 2) M M T I ( (7, 3) (6, 0) UV } 2 AB } isthemidpointofsegment.Find MN } PQ } 1, S

. Find . Find

x . atpoint

atpoint

2 8) R andmidpoint CB UV

if R if J . Find . Find AB UT 6. Find

5 5 A MN RQ 14.8meters. 4 } 2 1 x if if

yards. AM 1 M PQ JM 2 5 20 . of

5 5 15. 13. 11. M 14centimeters. 9. RS } 6

} 4 3

toﬁndthecoordinatesof

feet. R R G L x (4, 2)and (11, (3, 4), 2 ( 2 4 2, 2 2 C M 5),

8) and (3, M P (0, 2) 7. 2 ( 2 Date

Find 2) H 4, PM ( 2 2 ———————————— 4 3, 4) x MR

2 2 12 12) . Practice Workbook 2 2 x 1 Geometry 21 R 7 8 Name

Tell whetherthesegmentsarecongruent. The endpointsoftwosegmentsaregiven.Findeachsegmentlength. of thesegment. Find thelengthofsegment.Thenﬁndcoordinatesmidpoint Find thelengthofsegment.Roundtonearesttenthaunit. 24. 22. 20. 18. 16. Practice Workbook Geometry LESSON

1.3 AB MN } KL } CD } } ——————————————————————— 2 J : 4 : ( : ( : 2 A 2 K 2 C M (2, 6), 2, 3) 2, 4) 30123 ( ( 2 ( For usewiththelesson“UseMidpointandDistanceFormulas” Practice 2 2 2 4, 13), 2 1, 0), 1 1 1, 2 2 y y B 1 P 1 1 (0, 3) 2), (2, 1) K D (1, 3) L 1 ) (1, 3) N ( 2 ( 2 10, 6) x x

1, 2 continued 11) 45 67

19. 17. 25. 23. 21.

QR } OP } TU } RS } 2 2 : 9 :

: : y 1 R 2 T Q O 2 (5, 4), ( 82 B (5, 2), (6, y 2 (2, 2 1 4, 7 S 2 2 2 R (4, 4) 2 A 2), S 3) 6 (2, (10, 5) R 3), (0, 4) 2 (1, 5) Date P 2 5 (3, U 1) 2 ( 4 2 2 ———————————— x x 2 1, 1) 2) 3 2 2 2 1 0 1

Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Name D. C. B. A. The coordinatesaregiveninmiles. are: Dunkirk(0,0),Clearfield(10,2),LakeCity(5,7),andAllentown(1,4). usethemap.Thelocationsoftownsonmap In Exercises27–29, a.

29. 28. 27. 26. LESSON Find thedistancebetween eachpairoftowns. 1.3 b. The movie theaterishalfway between your houseandthemall,onsameroad. Distances is thebestrouteformarathon? marathon. Which ofthefollowing plans The mapisbeingusedtoplana26-mile Which two towns apart? arefarthest Which two towns areclosesttogether? Round tothenearesttenthofamile. ——————————————————————— Dunkirk toLake Cityto Allentown toDunkirk Dunkirk toLake CitytoClearfieldDunkirk Dunkirk toClearfieldLake Cityto Allentown toDunkirk Dunkirk toClearfield Allentown toDunkirk You walk atanaverage speedof3.2milesperhour. About how longwould it Draw andlabelasketch torepresentthissituation.How isyour far housefrom take you towalk tothemovie theaterfromyour house? the movie theater? For usewiththelesson“UseMidpointandDistanceFormulas” Practice Your onthesamestraightroad. houseandthemallare9.6milesapart continued Explain .

1 Dunkirk (0,0) Distance (mi) 1 Allentown (1,4) Date Clearfield (10,2) Lake City(5,7) ———————————— Distance (mi) Practice Workbook Geometry

9 10

Use thegiveninformationtoﬁndindicatedanglemeasure. appears tobe Give anothernamefortheangleindiagram.Tell whethertheangle names fortheangle.Thennamevertexandsidesof Use aprotractortomeasuretheanglenearestdegree.Writetwo Name

10. 8. 6. 4. 1. Practice Workbook Geometry LESSON Given

1.4 BC A ——————————————————————— QPN PQM JKN B (3 A x m

For usewiththelesson“MeasureandClassifyAngles” Practice

15) ABC acute ( x 8 D 1

7) , 94 8 C obtuse 8 9. 7. 5. , ﬁnd

, m PLK JML KMN right 2. CBD

, or OP . straight 11. M . K Given J (3

m x S 1 L QST

1) (2 8 3. x

Date 5

2 M

R 135 6) 8 T E ———————————— FG 8 , ﬁnd N P m QSR .

Then givethecoordinatesofapointthatliesininteriorangle. Plot thepointsinacoordinateplaneanddraw In thediagram, Find theindicatedanglemeasure. 15. 14. 13. 12. 21. 19. 16. LESSON

1.4 B d c b a A A ——————————————————————— 8 8 8 1 8 ( (2, 3), 2 y 4, 1 4 2 A For usewiththelesson“MeasureandClassifyAngles” Practice x B 3), 2 (3, 0), (3 D x y B 2 BD # ( ### C 2 6) $ C 1, 3),

bisects (2, 6) x x

C (4, 4) continued ABC 17.

. Find A B (5 x m (4 11) x ABC 22. 20. D 1)

. C A A ABC ( (6, 2), 2 2,

. Classifytheangle. d 2 8 B 4), 75 1 2 ( 2 8 18. y y B 1, 1 2 ( 2 2 Date

2, c 2), 8 2 A (8 ———————————— C x x 1), x (2, 3) a C 8 16) (3, D 160 B 2 (4 Practice Workbook 1) 8 x b 8 20) Geometry C 11 12 c. b. a. Name 25. 24. 23. Practice Workbook Geometry LESSON Let (3 1.4 values of Use only thelabeled angles inthediagram. angle. What isthemeasureof m of fourstreets.Inthediagram, Flags Streets angle and ——————————————————————— If angles. Identifythecongruent m Which anglesareacute?obtuse?right? BEC Intheﬂagshown, m x

For usewiththelesson“MeasureandClassifyAngles” Practice The diagram shows Thediagram theintersection RNS 1

5 QNR x 24) NR # ? ##

, m $ m bisects

representthemeasureofanobtuseangle. What arethepossible 5 CED QNS 30 8 , and , ﬁnd , and MNP continued m m MNP AED and QNP MNR m CED isastraight isaright AEB QNS . , ?

5 . 60 8 ,

M A E N P Cherry St. Raspberry St. Date 10 ———————————— th S St. Chestnut St. B C D R

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. angles. Giventhemeasureof 8. vertical angles usethediagram.Tell whethertheanglesare In Exercises8–12, 5. Find Name 12. 11. 10. 15. 14. 13. 9. 1. 1 and LESSON

Themeasure ofoneangleis38 Two alinearpair. anglesform The measureofoneangle is8timesthemeasureof Themeasureofoneangleisthreetimestheitscomplement.Find the 1.5 m measure ofeachangle. the otherangle.Find themeasureofeachangle. measure ofeachangle. m ——————————————————————— BD EB 2 and 4 and 5 and 4 and 1 and 1 ABC 2 arecomplementaryanglesand 5 For usewiththelesson“DescribeAnglePairRelationships” Practice A 80 and 2 3 9 8 5 3 8 x (3 , a

8 x

2 linear pair m C 10) CBD 8 2.

. m , or 1 8 6. 1, ﬁnd lessthanthemeasureofits supplement.Find the 5 neither

33 ABD 8 (5

x m

. C 2 22) 89 2 and 567 45 8 2 and 3. 13 (8 m x m

2 1 46) 3. 1 3 aresupplementary 5 8 72

7. Date

ABD ———————————— (2 4. x C

1 m 1) 8 1 Practice Workbook 5 (3 x 7

2 8 31) Geometry 8 13 14 Name

Tell whetherthestatementis Find thevaluesof 27. 25. 24. 23. 22. 19. 16. Practice Workbook Geometry A LESSON

and 1.5 m m m m An anglethathasasupplementalsocomplement. The supplementofanobtuseangleisacuteangle. Two alinearpair. anglesform complementary ——————————————————————— (14 (16 B B A A x x

B 20 5 5 5 5 1 2 For usewiththelesson“DescribeAnglePairRelationships” Practice arecomplementaryangles.Find

(6 (2 (4 y 4) 1.5 4) x 8 8 8 8

16.5 x x x x

2 2 2 (4 8 y 18) 75) 18) x 8 2 x and

8) 8 8 8

y . continued 20. 17. always

(12 (28 , y 6 sometimes x 1 x 2 8

30)

3 7) y 8 8 8 28. 26. (15 m (24 x

x 1 A m m m m 1 , or

and 75)

18) B B A A 8 never 8

5 5 5 5

m ( ( (2 (4 2 x

x x 1 B x 21. 18.

true. 1 1

. 1 36) 10) 34) Date

55) 8 (3 8 8 8 x ———————————— 1 (3

5 7) x y 8 5 ( 8 y 1 y (12 8 1

x (5 75) 8 2 x

8 2 41)

35) 8 8

diagram, identify twodifferentexamplesoftheindicatedtypeanglepair. Inthe one typeofrooftrussmadeoutbeamswood.Usethediagramto Roof trussescanhaveseveraldifferentlayouts.Thediagrambelowshows 38. 37. 36. 35. 34. 33. 31. 29. A LESSON

and 1.5 m m Angle ofelevation Complementary angles Complementary angles Supplementary m m Adjacent angles Linear pairangles Vertical angles plane ﬂiesclosertotheperson? is theangleofelevation affected asthe represents theangleofelevation. How horizontally acrossthesky and aplaneisﬂying horizontal. Inthediagram, and thelineofsightanobjectabove the is theanglebetween thehorizontalline ——————————————————————— B B A A

B 5 5 5 5 For usewiththelesson“DescribeAnglePairRelationships” Practice aresupplementaryangles.Find HBC (3 ( (2 ( x x

x x 1 1

2 1 and 100) 50) 223) 3) 8 8

8 An 8 BCE

angle ofelevation continued arerightangles. A Explain RST

I BC H 32. 30. m J

A ST m m m m and FE GF B B A A

5 5 5 5 m ( ( ( 6 x x 2 x B

8 1 1 4 . x 50) 5) L

1 Date 8 40) 8 R ———————————— 8 Not drawntoscale K Practice Workbook D Geometry

15 16 9. 8. 6. equilateral Classify thepolygonbynumberofsides.Tell whetherthepolygonis polygon, tellwhetheritis Tell whethertheﬁgureisapolygon.Ifitnot,explain why. Ifitisa Name 10. 4. 1. Practice Workbook Geometry LESSON The expressions Theexpressions (3 Thelengths(infeet)oftwo sidesofaregular quadrilateralarerepresentedby the

1.6 sides ofanequilateralpentagon. Find thelengthofasidepentagon. expressions 8 regular decagon.Find themeasureofanangledecagon. 3 m ——————————————————————— 3 m , For usewiththelesson“ClassifyPolygons” Practice 3 m equiangular x 3 m

2 3 m

2 6and4 2 x

x 1

1 63) , or 41and7 x convex

8 1 and(7 regular 22.Find thelengthofasidequadrilateral. 2. x

x or 2

2 . Explainyourreasoning. 40representthelengths(in kilometers)oftwo 45) concave 8 representthemeasuresoftwo anglesofa 5. 7. .

3. Date

————————————

Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Name Each figureisaregularpolygon.Findthevalueof Draw afigurethatfitsthedescription. Tell whetherthestatementis 22. 19. 17. 15. 13. 11. LESSON Aconcave pentagon Atriangleisconcave.

1.6 A quadrilateralthatisnotregular A quadrilateralisconvex. ——————————————————————— x ( x 2

1 1 x

30) For usewiththelesson“ClassifyPolygons” Practice 1 2 8 x

7 8 9 x 2

1 x

18. 2 14.

12. continued 23. 20. always 16.

13 x , 1 sometimes

27 Anequiangularhexagon thatisnotequilateral Aconvex heptagon Aregular polygon isequilateral. Anoctagonisregular. 3 x x x 2 2 , or

1 2 1 x

8 2 32 . x x never

2 1

52 8

24. 21. true. Date

———————————— x 2

12 (4 2 x x Practice Workbook (4 2 2

1 2 x 2

8) 61

1 Geometry 8

2 x 2

2) 8 17 18 Name

27. 26. 25. Practice Workbook Geometry LESSON

1.6 b. around theborderonetime? ribbon areneededtowrapthe ribbon aroundit.How many feetof decorate theframeby wrappinga triangle, asshown. You want to with awooden borderisaregular Parachutes Picture frames A ofafigurearegivenThe vertices below. using algebra. Then show thatthefigureisequilateral aconvexform polygon. Classifythefigure. Plot andconnectthepointssothatthey c. ——————————————————————— (3, 0), Determine the number of lines of symmetry inthecanopy. thenumberoflinessymmetry Determine How doesthisdiffer Classify thepolygon by thenumberofsides. andaprotractor Then usearuler from aregular octagon? whetherto determine thefigureisequilateral,equiangular, orregular. Is theshapeofcanopy a For usewiththelesson“ClassifyPolygons” Practice B (3, 6), Thecanopy ofaparachuteisshown inthediagram. Apictureframe C (2, 3), D continued (4, 3) convex or concave polygon?

1 y 1 ( 3 x

1 16 ) in. Date (7 x ———————————— x

8)in .

Graph thepatternonanumberline. Describe apatterninthenumbers.Writenextnumberpattern. Sketch thenextﬁgureinpattern. Name 11. 9. 7. 5. 3. 1. LESSON

113,224,335,446,. 2,5,11,23,. 3, 0, 2.1 } 3 1 ———————————————————————

, , } 4 3

, , 2 } 5 5 , , 3, For usewiththelesson“UseInductiveReasoning” Practice } 6 7

, . 2 6, .

12. 10. 4. 2. 8. 6.

2, 3,5,7,11,. 1, 4,9,16,. 4, 6,9,13,18,. } 8 7

, , } 7 6

, , } 6 5

, , } 5 4

, . Date ———————————— Practice Workbook Geometry 19 20 Name Show theconjectureisfalsebyﬁndingacounterexample. the nextobject? The ﬁrstthreeobjectsinapatternareshown.Howmanysquares 13. 18. 17. 16. 15. Practice Workbook Geometry LESSON Thesquarerootofanumber If Thedifference oftheabsolutevalue oftwo numbersispositive, meaning Thequotientoftwo whole numbersisawhole number. 2.1 | ——————————————————————— a m |

Þ 2

For usewiththelesson“UseInductiveReasoning” Practice 2 | b 1, then | >0. } m 1 m

<1. continued x isalways lessthan

14. x

. Date ————————————

Write afunctionrulerelating 21. 19. 24. 23. LESSON

2.1 prediction be? you topredictthenumberofbacteriaafter7doubling periods. What would your table shows thenumberofbacteriaafter Bacteria Growth less than 1 gram oftheisotope? less than1gram which hasahalf-lifeof3days. How many days willittake beforethereis of theisotopetodecay. Suppose you ofPlatinum-191, begin with25grams Chemistry ——————————————————————— y x y x billions ofbacteria n (periods) 432 123 1827 3 12 For usewiththelesson“UseInductiveReasoning” Practice Thehalf-lifeofanisotopeistheamounttimeittakes forhalf Supposeyou arestudyingbacteriainbiology class. The

continued 63 4128 64 32 16 8 4 5 4 3 2 01 x and y . n doubling periods. Your teacherasks 22. 20.

y x y x 2 . 0.25 0.5 1 4 12 123 5 2 3 Date 2 ———————————— 1 Practice Workbook Geometry 21 22 9. counterexample. Decide whetherthestatementis Write theconverse,inverse,andcontrapositiveofeachstatement. Rewrite theconditionalstatementinif-thenform. Name 10. 8. 7. 6. 5. 4. 3. 2. 1. Practice Workbook Geometry LESSON Two linesintersectin atmostonepoint. If If Theequation4 If Ifyou like hockey, thenyou gotothehockey game. when thereisgasinthetank. Thecarruns Anobtuseangleisanthatmeasures morethan90 isfull. Thereare12eggs ifthecarton Itistimefordinnerifit6 2.2 ——————————————————————— m x x isodd, then3 2

5 A For usewiththelesson“AnalyzeConditionalStatements” Practice 36,then

5 122°,thenthemeasureofsupplement x

x 2 x mustequal18or isodd. 3 5 12 1 P 2 . M x . hasexactly onesolution. true 2 18. or false . Iffalse,providea 8 andlessthan180 A is58°. Date ———————————— 8 .

Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Decide whetherthestatementisavaliddefinition. and itsconverse. Rewrite thebiconditionalstatementasaconditional combine thestatementstowriteatruebiconditionalstatement. Write theconverseofeachtruestatement.Ifisalsotrue, Name 19. 18. 17. 16. 15. 14. 13. 12. 11. LESSON Ifananimalisapanther, thenitlives intheforest. Iftwo circleshave thesamediameter, thenthey have thesamecircumference. Iftwo anglesaresupplementary, thenthesumoftheirmeasuresis180 Ifananglemeasures30 Iftwo anglesarenotadjacent,thenthey angles. arevertical Iftwo angleshave thesamemeasure,thenthey arecongruent. Ifanumberisdivisible by 2and3,thenitisdivisible by 6. Apointisamidpointofsegment ifandonly ifitdivides thesegment intotwo Two ifandonly rightangles. ifthey linesareperpendicular intersecttoform 2.2 congruent segments. congruent ——————————————————————— For usewiththelesson“AnalyzeConditionalStatements” Practice 8 , thenitisacute. continued Date 8 . ———————————— Practice Workbook Geometry 23 24 answers toExercise20–22. In Exercises23and24,usetheinformationintableabove for eachtypeofsaxophone. usetheinformationintabletowriteadefinition In Exercises20–22, Name 24. 23. 22. 21. 20. -a losxpoe18830 622 415 138 103 69 E-flat altosaxophone B-flat tenorsaxophone E-flat baritonesaxophone ntuetLwrlmt(z Upperlimit(Hz) Lowerlimit(Hz) Instrument Practice Workbook Geometry LESSON Ifthefrequency ofasaxophonewas 210Hz,what couldyou conclude? Ifthefrequency ofasaxophonewas 95Hz,what couldyou conclude? E-flataltosaxophone B-flattenorsaxophone E-flatbaritonesaxophone 2.2 ——————————————————————— For usewiththelesson“AnalyzeConditionalStatements” Practice continued Frequency (cyclespersecond) Date ————————————

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. law wasused.Ifitdoesnot,writeinvalid. the LawofDetachmentorSyllogism.Ifitdoes,statewhich Determine ifstatement(3)followsfromstatements(1)and(2)byeither Name 1. 6. 5. 4. 3. 2. LESSON (1)Ifyou withicecream. ordertheapplepie,then itwillbeserved (1) All 45 (1)Ifananglemeasuresmorethan 90 (1) If (1)Ifyou eattoomuchturkey, thenyou willgetsick. (1)Ifyou wear theschoolcolors,thenyou have schoolspirit. 2.3 (3) Matthew was icecream. served (2) Matthew ordered the applepie. (3) (2) (3) (2) (3) If (2) If (3) Kinsley atetoomuch turkey. (2) Kinsley gotsick. (3) Ifyou wear theschoolcolors,thenteamwillfeelgreat. (2) Ifyou have schoolspirit,thentheteam feelsgreat. ——————————————————————— m A A ABC For usewiththelesson“ApplyDeductiveReasoning” Practice and ABC > 2 isacute,then 2 isacute,then 3 isobtuse,then 8

isnotacute. anglesarecongruent.

B 5 B 120 are45 8 8 angles. 3 isobtuse. 4 isacute. 4 isacute. 8 , thenitisnotacute. Date ———————————— Practice Workbook Geometry 25 26 Name Explain In Exercises11and12,statewhethertheargumentisvalid. 9. 8. 7. used toreachtheconclusion. In Exercises7–10,decidewhether 12. 11. 10. Practice Workbook Geometry LESSON 2.3 driver education.SoBrandonisasophomore. Katie knows thatallsophomorestake driver educationinherschool.Brandontakes SoJeffafternoon. didnotdohischoresonSaturday morning. to play videogameslaterthesameday. Jeff doesnotplay videogamesonSaturday Jeff knows hewillnotbeallowed that ifhedoesnotdohischoresinthemorning, has hisdriver’s license. Therefore, Anthony tookdriver’s education. driver’s educationtogetyour license. Anthony lives inNevada, is16years old, and If you live inNevada andarebetween theagesof16and18,thenyou musttake this Wednesday. macaroniandcheeseforlunch lunch. Danaconcludesthatthecafeteriawillserve For thepastthree Wednesdays, macaroniandcheesefor thecafeteriahasserved more thanallotherbrands. brands thatJoshknows ofcostlessthanBrandX.Joshreasonsthat Y costs Josh knows thatBrandXcomputerscostlessthan Y computers. All other Natalie. Angela reasonsthat Walt istallerthanNatalie. Angela knows that Walt istallerthanPeter. Shealsoknows thatPeter istallerthan ——————————————————————— yourreasoning. For usewiththelesson“ApplyDeductiveReasoning” Practice continued Explain inductive yourreasoning. or deductive reasoningis Date ————————————

E. C. A. The mallisopen. If Jodigoesshopping,thenshewillbuyapizza. If themallisopen,thenJodiandDanwillgoshopping. If Dangoesshopping,thenhewillbuyapretzel. you knowtheconclusionis usethetruestatementsbelowtodeterminewhether In Exercises13–16,

15. 13. 17. LESSON Jodiboughtapizza. Danboughtapizza. 2.3 D. B. “If thereisafire,then?.” the robotinorder. Then usetheLaw ofSyllogism tocompletethestatement, fire-fighting robotisunderdevelopment. Write thefollowing statementsabout Robotics ——————————————————————— Ifthereisafire,thentherobotsenseshighlevels of smoke andheat. Iftherobotsenseshighlevels ofsmoke andheat,thenitsetsoff afirealarm. If therobotconcludesthereisafire,thenitlocatesfire. If therobotlocatesfire,thenextinguishes thefire. If therobotsetsoff thenitconcludesthereisafire. the firealarm, For usewiththelesson“ApplyDeductiveReasoning” Practice Becauserobotscanwithstandhighertemperaturesthanhumans,a continued true or false . Explain 16. 14. JodihadsomeofDan’s pretzel. JodiandDanwent shopping. yourreasoning. Date ———————————— Practice Workbook Geometry 27 28 of thestatement. Use thediagramtostateandwriteoutpostulatethatverifiestruth Draw asketchtoillustrateeachpostulate. Name (labeled 7. 6. 5. 4. 3. 2. 1. Practice Workbook Geometry LESSON The points The planes The points The points Iftwo planesintersect,thentheirintersectionisaline. Iftwo pointslieinaplane,thenthelinecontainingthemliesplane. Iftwo linesintersect,thentheirintersectionisexactly onepoint. 2.4 Therefore, line (labeled (labeled ——————————————————————— For usewiththelesson“UsePostulatesandDiagrams” Practice n m R ). ). ). E E E Q and and , and F m , and liesinplane F F R lieinaplane lieonaline intersectinaline H lieinaplane R . R .

E F H m Date Q R ———————————— n

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Name true In Exercises12–19,usethediagramtodetermineifstatementis 9. 8. point wall ofyourclassroomasline thinkoftheintersectionceilingandfront In Exercises8–11, 19. 18. 17. 16. 15. 14. 13. 12. 11. 10. LESSON Points Isthereaplanethatcontainspoints Isthereaplanethatcontainsline Istheremorethanoneplanethatcontains bothpoints Istheremorethanonelinethat containsbothpoints Planes Points 2.4 or FG @ FG @ ——————————————————————— ## ## A GCA ABD EBA $ $ false andthecenterofceilingaspoint

and > plane isarightangle. A E and and H For usewiththelesson“UsePostulatesandDiagrams” Practice DE @ , , and . ## B G $ , , and intersect. H D CBD K , and EBC intersectat A arecollinear. are congruent angles. arecongruent are vertical angles. arevertical J arecoplanar. continued @ AB ## $ .

k . Thinkofthecenterﬂooras k andpoint A , B , andapointonthefrontwall? A ? B

. A and A H and J B ? B ? AB D Date G ———————————— E C F K Practice Workbook Geometry 29 30 Name c. a.

20. Practice Workbook Geometry LESSON 2.4

d. b. Building Eisduewest ofBuildingC. Buildings BandDareonStreet3. Building DissoutheastofB. Buildings BandCareonStreet2. Building CisdueeastofB. Buildings A andBareonStreet1. Building Bisduesouthof A. (a)–(e). neighborhood. Usethestatementstocompleteparts Neighborhood Map e. ——————————————————————— Isbuilding Ebetween buildings BandC? What streetisbuildingEon? WheredoStreets1and2intersect? DBE Classify the angle formed byClassify theangleformed Streets1and2. Draw oftheneighborhood. adiagram formed by formed Streets2and3isacute. For usewiththelesson“UsePostulatesandDiagrams” Practice Afriende-mailedyou thefollowing statementsabouta continued Explain . Date ————————————

Complete thelogicalargumentbygivingareasonforeachstep. Name

10 1. 5. 4. 3. 2. LESSON 8 5(2

2.5 m m AC AB AC 10 m @ m AC AB ——————————————————————— ## 10 $ x x

5 5 5 5 1 1 > 2 2 AEB x 2

5 5

5 2 @ EF 5 5 AB AB BC ## 1) For usewiththelesson“ReasonUsingPropertiesfromAlgebra” Practice x x 90

90 5 $

m AB 5

5 5 5 x x ,

Given 1 1

CD @ 5 5

5 5 8

8 2

## ) 2 2 2

m m m m m m

2 9 9 AB BC 7 7 9 $ 2 15 10 1

x x > x x

BED

BEC AEB AEC AEC BEC

1 1 2 1 @ EF ## 2 Given 2 2 2 1 Given 15 7 7 $ Given

5 5 5 5 5 5

m m m m m m CED CED CED BEC BED AEB Given

1 1 1

m m m BEC BEC BEC

c. b. a. c. b. a. c. b. a. e. d. c. b. a. c. b. a. ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

A E Date E A ———————————— 12 B A BD B C D Practice Workbook C C Geometry F

31 32 Name 9. 8. 7. 6. Use thepropertytocompletestatement. 12. 11. 10. Practice Workbook Geometry LESSON Transitive ofEquality:If Property Reﬂexive of Property Angle Measure: 2.5 of points AB attheright: aboutthediagram information Distance ofEquality:If Multiplication Property ofEquality:If Substitution Property ofEquality:If Symmetric Property ofEquality:If Addition Property ———————————————————————

CD For usewiththelesson“ReasonUsingPropertiesfromAlgebra” Practice You aregiven thefollowing C , CD and

5 E

. OE Explain . Find thecoordinates continued your reasoning. x CD

5 BC m 3,then14

m 5

m 5 A

B 5 A

5 45 and? , then?. 5 ?. 45 8 1 , then3( 8

, then?( x

?. 5 m

D RS ( 2 , then?. A 3, 1) ) m 5 ?. A C Date ) 5 15 OE ———————————— 8 y . A B (3, 2) (6, 6) x

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Name m m m m following aboutthecirclegraph. represents thepercentoftotalvotes thateachcandidatereceived. You know the belowThe circlegraph shows theresultsofelection.Eachsectorongraph Statistics usethefollowinginformation. In Exercises16–18, distance (inmiles)hetravels isgiven by thefunction Hewalks 0.11mi/min. and therestoftimerunning. 0.06mi/minandruns The total Treadmill usethefollowinginformation. In Exercises13–15,

18. 17. 16. 15. 14. 13. LESSON 1 1 Usethetable fromExercise thetimespent 14tograph Make atable thatshows thetimespentwalking for Solve theformula How many votes dideachcandidatereceive iftherewere atotalof315votes? Whatpercentofthevote dideachcandidatereceive? Find theanglemeasureforeachsector. 2 2 2.5 5 1 to thetimespentwalking asdistanceincreases? walking asafunction ofthedistancetraveled. What happens 2.7, 3,3.7,4.3,and4.5. for thefollowing distancestraveled: 5 1 ———————————————————————

m m m m Thestudentsataschoolvote foroneof fourcandidatesforclasspresident. Markworks outfor45minutesonatreadmill.Hespends 4 2 4 3 For usewiththelesson“ReasonUsingPropertiesfromAlgebra” Practice 1 5

200 m 3 8 1

m t andwriteareasonforeachstep. 4 5 continued 360 8

5 0.06 t

1 4 0.11(45 3 1 t 2 minuteswalking Date

Time spent walking (minutes) 2

10 15 20 25 35 40 45 50 30 t 0 5 ). ———————————— t . 3.5 2.5 0 Distance (miles) Practice Workbook 4.5 Geometry D

33 34

2. completetheproof. In Exercises1–4, Name

1. Practice Workbook Geometry LESSON

2.6 6. 5. 4. 3. 2. Statements 1. GIVEN: GIVEN: 6. PROVE: PROVE: 2. 1. 3. 5. 4. Statements ———————————————————————

? HI m m m m HI } IJ } IJ HI

1 3 and

> 5

5 > 5 1 1 3 1 >

9 9 For usewiththelesson“ProveStatementsaboutSegmentsandAngles” Practice

JH }

9 9 IJ 5 1 1 1 JH }

HI m HI }

m m m m

3 and 1

5 r opeetr. 2 arecomplementary. > 1 > 9, 3 2 2 2

1 JH }

5 5 5

IJ m

3 90 90 m

2 arecomplementary. 5 8 8 2 9,

3 5 1 IJ } 90

m >

JH } 5. 6. Reasons 1. 2. 3. 4. 2 ? ? ? ? ? Deﬁnition of congruent segments Deﬁnitionofcongruent

6. 5. 4. 3. 2. 1. Reasons ? ? ? ? ? ? Date HI ———————————— 3 J 2 1

Name

3. 4. LESSON 2.6 6. 5. 4. 4. 3. 3. 2. 2. 1. 1. GIVEN: GIVEN: Statements Statements PROVE: PROVE: ———————————————————————

AS SK AL m AL LS m AL 2 4

5 5 1 1 1 5 2 4 > > For usewiththelesson“ProveStatementsaboutSegmentsandAngles” Practice

5 5 LS LK

LS LS LS SK AL m m AS 120 120

4 5

5 5 5 5 5 4 2

LK AS SK 8 8 5

, 5 SK LK

120

120 1 2

LS > 8 8 ,

5, continued 2 > 5, 4 > 5 6. 5. 4. 4. 3. 3. 2. 2. 1. 1. Reasons Reasons ? ? ? ? ? Deﬁnition of congruent angles Deﬁnitionofcongruent ? ? ? ? Date LS AL ———————————— 6 5 4 1 Practice Workbook 2 3 Geometry K 35 36 Name

9. Solve for 7. 5. Practice Workbook Geometry LESSON

2.6 that Optical Illusion You measure you needtomake surethattherow heights arethesame. decide tomake thisdesignyourself. You draw thegrid, but and same measure.For instance, wasgrid used.Inthegrid, row corresponding heightsarethe ——————————————————————— AC ABD W (14 (11 UW }

VW } > x x D x

For usewiththelesson“ProveStatementsaboutSegmentsandAngles” Practice usingthegiveninformation. >

> >

10)

Z 8)

YX } ZX } 8 8 DBE UV } WZ B . . Write anargument that allows you toconclude (11 To createtheillusionatright,aspecial ,

, UW } x 1 EBC E ,

5) ZY } (9 8 x

, and

continued > 1

UV } 4)

8 DBE ZX } and

. You ﬁndthat

ZY } are congruent. arecongruent. You

Explain 8. 6. UV }

yoursteps.

KM KP } FG } 5 > LN x

2 ZY }

GH > >

F PN } FJ }

, ,

P FJ } KP

5 Date W

U X V Y Z JH } 18

———————————— J 7 x x 2 2

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. complementary angles. and complementary angles. where oneanglemeasures42 can bedetermined. Make asketchofthegiveninformation.Labelallangleswhich Use thediagramtodecidewhetherstatementis Name 9. 7. 5. 2. 1. 4. 3. LESSON Congruent linearpairs Congruent angles Adjacentcomplementary If If

2.7 m m ——————————————————————— ABC m m 1 1 1 1 1 1 DBE and For usewiththelesson“ProveAnglePairRelationships” Practice

5 5 m m 47 47 aeajcn areadjacent 4 3 8 8 CBD , then , then 5 5

m m areadjacent m m 2 2 1 1 3 2

m m CBD 5 5 47 43 8 3. 4. where oneanglemeasures42

8 8 . . 10. 6. 8.

Nonadjacent supplementary angles Nonadjacent supplementary Vertical angleswhich measure42 1 and 3 and 1 and true 1 or 4 3 are vertical angles. 3 arevertical 4 arecomplementary. 2 arecomplementary. 2 3 false Date . ———————————— 8 Practice Workbook 8 Geometry 37 38 Name

Give areasonforeachstepoftheproof. the diagram. Find thevalueofvariablesandmeasureeachanglein 13. 11. 15. Practice Workbook Geometry LESSON

2.7 5. 4. 3. 2. Statements 1. GIVEN: PROVE: ———————————————————————

(13 1 1 2 3 2 (4 x > > > > > 4

y (21 For usewiththelesson“ProveAnglePairRelationships” Practice 1

y 1

9) 8

x 2)

8 4 2 4 4 3 2

2 (17 1 8 3) > > 2(3 y (15 8

2 y x 9)

3 4 2 (5

2 25) 8 x 1)

1 8 8 1) continued 8

14. 12.

5. 4. 3. 2. 1. Reasons ? ? ? ? ? (4 x (16 2(

1 y 10) y

7 2 x 25) 8 27) 8 8 13 13 8 Date (5 x y (2 1 8 8 x y

———————————— 2 18) 30) 23 8 8 4

statement with<,>,or In thediagram,

20. 19. 18. 17. 16. LESSON

2.7 7. 6. 5. 4. 3. 2. 1. GIVEN: Statements PROVE: m m m m ———————————————————————

m m m m 2 9 ?3( 6 6 3 and 1 1 and 1 1 1 3 3 1 1 > For usewiththelesson“ProveAnglePairRelationships” Practice

1 1 5 1 m m m

m m m m 3,

1 1 and 3 and 3 ? 8 ? 7 ? r opeetr. 4 arecomplementary. r opeetr. 2 arecomplementary. m > 4 2 3, 2 1 isarightangleand

2 5 5 5 6) m > 3, 90 90 90 m m m 2 arecomplementary.

4 arecomplementary. 2 8 8 8 5

4 2 5 1 2 4 . >

1 1 continued m

m m 4 4 3 5 m

6 5 36

7. 6. 5. 4. 3. 2. 1. Reasons 8 ? ? ? ? ? ? ? . Completethe 57 45 1 3 2 6 Date 9 8 ———————————— 1 2 3 4 Practice Workbook Geometry

39 40 9. 8. 7. 6. plane(s) appeartoﬁtthedescription? Think ofeachsegmentinthediagramaspartaline.Whichline(s)or 5. 4. 3. 2. statement with Think ofeachsegmentinthediagramaspartaline.Complete Name 10. 1. Practice Workbook Geometry LESSON Plane(s) paralleltoplane toplane Plane(s)perpendicular Line(s)skew to to Line(s)perpendicular Line(s)parallelto Plane Plane 3.1 QT @ WZ @ WZ @ ——————————————————————— ## ## ## $ $ $ and

and and RQT WZR For usewiththelesson“IdentifyPairsofLinesandAngles” Practice @ YS @ @ ZR ST ## ## ## $ $ $ andplane are?.

andplane are?.

are?. parallel CD @ ## $ EH @ andcontainingpoint ## $ YXW

SYZ , skew EH @ FGC ## are?. are?. $

, or AEH perpendicular F

. W F E GC XY H T Date ———————————— D Z A R B S

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Name Copy andcompletethestatementwith usethemarkingsindiagram. In Exercises17–20, exterior Classify theanglepairas 24. 23. 22. 21. 20. 19. 18. 17. 16. 15. 14. 13. 12. 11. LESSON Name a pair of perpendicular lines. Nameapairofperpendicular Nameapairofparallellines. Iftwo linesarecoplanar, thenthey are?parallel. Iftwo linesintersect,thenthey are?perpendicular. Ifonelineisskew toanother, thenthey are?coplanar. Iftwo linesareparallel,thenthey ?intersect. Is Is 3.1 ——————————————————————— 10 and 1 and 4 and 8 and 8 and 6 and OL @ OL @ ## ## , or $ $

> i

For usewiththelesson“IdentifyPairsofLinesandAngles” Practice @ TR

consecutive interior @ TR ## ## $ 10 13 16 16 9 $

? 13

? Explain Explain . . corresponding continued angles. sometimes , alternate

, interior 12 always

9 4 O 1 11 10 3 2 T , , or P alternate Date L never 16 13 ———————————— M 8 5 15 14 N . R 7 6 V S Practice Workbook Geometry 41 42 Name true Use thediagramofﬁreescapetodecidewhetherstatementis parallel toline Use constructiontoolstoconstructalinethroughpoint Copy thediagramandsketchline. 29. 34. 33. 32. 31. 28. 27. 26. 25. Practice Workbook Geometry LESSON The planes containing the platforms outsideofeachpair Theplanescontainingtheplatforms outsideofeachpair Theplanescontainingtheplatforms Theplanescontainingthestairsareparalleltoeachother. outsideofeachpair Theplanescontainingtheplatforms Line through Line through Line through Line through 3.1 or of windows areparalleltotheground. side ofthebuildingwith ﬁreescape. of windows totheplanecontaining areperpendicular the stairs. of windows totheplanescontaining areperpendicular ——————————————————————— false For usewiththelesson“IdentifyPairsofLinesandAngles” Practice . m P M N M . P andparallelto and perpendicular to andperpendicular and perpendicular to andperpendicular andparallelto continued m

MN @ NP @ ### ## $ $

. . MP @ MP @ ## ## $ $ .

30.

N P thatis Date ———————————— P M m

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Find Find theanglemeasure.Tell whichpostulateortheorem youuse. Name 8. 5. 2. 1. 4. 3. LESSON If If If If

3.2 m ——————————————————————— m m m m 1 and 1 6 2 4 For usewiththelesson“UseParallelLinesandTransversals” Practice 1 5 5 5 5 12 50 123 130 45 60 m 56 8 8 8 , then 8 , then 8 8 , then , then 2. 2 m m m m 5 6 3 7 5 5 5 5 ?. ?. ?. ?. 9. 6. 1 117 2 120 1 8 2 8

10. 7. 3 Date 1 2 5 4 7 8 ———————————— 6 80 1 8 2 1 2 108 Practice Workbook 8 Geometry 43 44 Name Find thevalueof Find thevaluesof 20. 17. 14. 11. Practice Workbook Geometry LESSON

3.2 ——————————————————————— 75 y 80 8 8 For usewiththelesson“UseParallelLinesandTransversals” Practice ( 8 x 75 y (5 8 1 8 x x x 15) 8 110 8 2 x 8 10) 8 x .

and 8

y . continued 21. 18. 15. 12.

3 x 68 8 x 120 8 8 y x y 8 2 8 8 8 106 x 8 8

16. 13. 22. 19. Date

(2 105 x ———————————— 2 95 8 4) y 8 8 y 8 8 ( x x x 8 2 8 2) 92 8 8

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Name p Statements PROVE: GIVEN: completethetwo-columnproof. In Exercises23–31, p m m q m

> > i 1 1 isarightangle. sargtage 2 isarightangle.

r LESSON

1 1 > 2 q r 3.2

5 5

5 ——————————————————————— 90 90 m 2

p p 8

2 For usewiththelessonUse“ParallelLinesandTransversals” Practice

q r , q

Reasons 31. 30. 29. 28. 27. 26. 25. 24. 23. ? ? ? ? ? ? ? ? ? continued 2 1 p r q Date ———————————— Practice Workbook Geometry 45 46 Find thevalueof parallel? Ifso,statethepostulateortheoremyouwoulduse. Is thereenoughinformationtoprovethatlines Name 7. 4. 1. Practice Workbook Geometry LESSON

3.3 n ——————————————————————— m 4 For usewiththelesson“ProveLinesareParallel” Practice x 2 8 x 58 8 100 (6 8 x 122

8 2 x 44) 8 thatmakes 8 q p n m

8. 5. 2. m

n . (5 x

1 85 23) 8 (7 8 60 x ( x 110

25 8 1

1 13) 8 p 1) 8 and n 8 8 q p m

m q

are n

3. 9. 6. Date ———————————— ( x

2 80 15) 82 8 ( 8 8 x

1 x 8 120 20) 8 m 8 m q p n n

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Name Statements PROVE: GIVEN: completethetwo-columnproof. In Exercises14–18, choosethewordthatbestcompletesstatement. In Exercises10–12, p g 13. 12. 11. 10.

i i 2 1 1

r h LESSON Iftwo linesarecutby anglesare( atransversal sothecorresponding Iftwo linesarecutby atransversal sotheconsecutive interioranglesare( Iftwo linesarecutby interioranglesare( atransversal sothealternate > > > 3.3

Explain row isparalleltotherow immediately next toit. Gardens supplementary supplementary supplementary

——————————————————————— 3 2 3

For usewiththelesson“ProveLinesareParallel” Practice h, r why theﬁrstrow isparalleltothelastrow. Agardenhasﬁve rows ofvegetables. Each 1 > , , ,

complementary complementary complementary 2

18. 17. 16. 15. 14. Reasons ? ? ? ? ? continued ), thenthelinesareparallel. ), thenthelinesareparallel. ), thenthelinesareparallel.

13 Date congruent congruent gh 2 ———————————— congruent , r r r r r 1 2 5 4 3 ,

Practice Workbook , r p Geometry 47 48 Name Statements PROVE: GIVEN: completethetwo-column proof. In Exercises19–23, p n 24.

i i 2 1 1 Practice Workbook Geometry

r m LESSON

> > > 3.3

Railroad Tracks n intersect asshown. How doyou know thatline

——————————————————————— isparalleltoline 3 2 3

For usewiththelesson“ProveLinesareParallel” Practice m, r 1 >

Two setsofrailroadtracks

2 m 23. 22. 21. 20. 19. Reasons ? ? ? ? ? ? continued

s nm t 1 Date 3 ———————————— m 2 n

r p

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Find theslopeofeachline.Arelinesperpendicular? Find theslopeofeachline.Arelinesparallel? Find theslopeoflinethatpassesthroughpoints. Name 7. 4. 1. LESSON

3.4 ——————————————————————— B C D 1 y For usewiththelesson“FindandUseSlopesofLines” Practice A B 1 2 1 y y 1 C B A A D 3 x x x 8. 5. 2. C B 1 D A D y 1 1 y 1 1 A B y 1 A C B x x x

3. 9. 6. Date A D ———————————— A C A D 1 2 1 y y y 1 1 1 Practice Workbook C B B B Geometry x x x 49 50 Name

ie2 2 ) 5 ) ie2 2 ) 4 ) Line2:(4,0),(5,3) Line 2:(2,1),(4,1) Line2:(4, Line2:(2,1),(5,5) Line2:(0,0),(3,1) Graph thelineperpendicularto Graph thelineparallelto Tell whethertheintersectionof or Tell whetherthelinesthroughgivenpointsare 22. 25. 20. 16. 13. 10. 18. Practice Workbook Geometry neither LESSON Line1:( Line1:( 3.4 A A A ——————————————————————— A ( (5, 4), ( 2 2 8, 17), 8, 3), . For usewiththelesson“FindandUseSlopesofLines” Practice B 2 2 P B 1 1 ( B 2 3, 4),( 1, 2),(2,3) P B (1, 2), y y 3, 20), ( 1 1 2 5, 18), A B 2 C 3, 1) C (0, 9), x x (9,

C (6, 11), 2 continued 2), D ( 2 26. 23. 14. 11. D AB 1, 0) (6, 4) D AB @ Line1:( Line1:(0,1),(1,3) thatpassesthroughpoint ### (5, 8) $ and AB B P thatpassesthroughpoint A A CD @ ### 2 1 2 $ formsarightangle. 5, 2),( 2 17. 21. 19. y y ) 5 ) Line 2:( 1), (5,2) 1 1 P B

A A A 2 (3, 2), ( (7, 12), 2 2, 2) x x parallel 7, 3),

B B (5, 10), B (1, 5), ( 15. 12. 27. 24. , 2 P perpendicula 10, 15), Date Line1:( Line1:(

. C C (7, (10, ———————————— y 1 P 2 C . A 2 1 4), ( 1 2 7), 2 2 2 A y 1, 5), 1 D 2, 2),(0,4) 2, 5),(1,4) 5, 0),( B D P r, r, (3, (3, P 2 D 2 B 2 3) (4, 35) 1) 3, x x 2 2)

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Name Line Line Line In Exercises28and29,considerthethreegivenlines. 29. 28. 31. 30. LESSON Whichlineisleaststeep? Whichlineismoststeep?

3.4 c b a Find theheight escalator, you have moved ahorizontaldistanceof90feet. 3 feetyou move horizontally. When you reachthetopof Parallelograms Escalators why theﬁgureshown isaparallelogram. ﬁgure whose oppositesidesareparallel. : throughthepoints(2,0)and(0,3) : throughthepoints(2,0)and(0,5) : throughthepoints(2,0)and(0,1) ——————————————————————— For usewiththelesson“FindandUseSlopesofLines” Practice On anescalator, you move 2 feetvertically forevery h oftheescalator. A parallelogram isafour-sided continued Explain

A B

Date 1 D y 1 ———————————— C x

90 ft Practice Workbook h ft

Geometry 51 52 to thelinewithgivenequation. Write anequationofthelinethatpassesthrough point Write anequationofline Name 7. 4. 1. Practice Workbook Geometry LESSON

3.5 P ——————————————————————— A ( 2 2, 0); For usewiththelesson“Write andGraphEquationsofLines” Practice 2 y A

y 5 1 1

y 2 1 } 2 1 B B

1 x x 6 AB inslope-interceptform. 8. 5. 2. P A (3, 9); A y B

1 5 B y 4 1 1 x y

2 1 8 x x

P andisparallel 3. 9. 6. Date P ( 2 ———————————— A 2 5, y 2 1 A 4); 1 y y 1

2 B B 2 x x x

2 10

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Name perpendicular toline Write anequationofthelinethatpassesthroughpoint to line Write anequationofthelinethatpassesthroughpoint perpendicular tothelinewithgivenequation. Write anequationofthelinethatpassesthroughpoint 16. 13. 10. LESSON

3.5 P ——————————————————————— B (5, 20); AB 1 B . y For usewiththelesson“Write andGraphEquationsofLines” Practice 1 A P 1 y

5 P y 1

} 2 1

A 1 8 AB x x

. continued 17. 14. 11.

P A (4, 5); B y A P

2 5 y

1 2 1 B y } 3 1 1

2 P 6 x x

P P P andis andisparallel andis 15. 12. 18. Date

P (3, 5); ———————————— P y A

1 1 5 y y 4 1 1 Practice Workbook B P B A Geometry x x 53 54 Name

Graph theequation. 22. 19. 25. Practice Workbook Geometry LESSON

2( 3.5 Country Club 2 y line. club.joining acountry Write anequationofthe ——————————————————————— -intercept oftheline. x 2

x 2

Explain 1 1)

For usewiththelesson“Write andGraphEquationsofLines” Practice y

5 1 1 5

y y 2 2 themeaningofslopeand 1 1 y 1 The graph modelsthetotalcostof Thegraph

x x

continued 23. 20.

x y

2 2 4 3 1 5 5 y 1 0 2 1 3 y x 1

1 2

x x

Cost (dollars) 4000 4500 5000 5500 6000 6500 7000 7500 8000 y 0 Membership Cost 21. 24. 023 4567 1 Date

2 (5, 7500) y

y 1

Months ———————————— 2 (3, 6500) 6 4 5 5 4 1 1 2 x y y 1 1 x

x x

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Find thevalueof your conclusion. What canyouconcludefromthegiveninformation?Statereasonfor Name

7. 4. 1. LESSON

3.6 ——————————————————————— 1 >

For usewiththelesson“ProveTheoremsaboutPerpendicularLines” Practice ( ( 2 12 x x

1 2 25) 15) x 8 8 . z s

8. 5. 2.

(3 >

x 51 m

1 8

(2 6) x

43 12 8 2 m 11) 8 n

3. 9. 6. Date

C # BA BA B ## ( x $

————————————

1 2 > 5)

( BC # x 1 ## 2

8 2 $ x

8 15) x 8 8 Practice Workbook A Geometry 55 56 Name nearest tenth. Find thedistancefrompoint usethediagram. In Exercises16–18, Find themeasureofindicatedangle.

19. 14. 12. 10. 18. 17. 16. Practice Workbook Geometry LESSON Is Is Is 3.6 ——————————————————————— 1 5 3 s m r

i i c

i t s

? n ? For usewiththelesson“ProveTheoremsaboutPerpendicularLines” Practice ? 1 y 1 A x

continued A 20. 15. 13. 11. toline

6 4 2 c A . Roundyouranswerstothe 1 y c 1

21. 5 rst 3 6 Date

4 2 60 1 ———————————— A 8 1 y 1 c n m x

22. 25. LESSON

3.6 d. b. in feet. Maps c. a. ——————————————————————— 100 300 500 700 Find Find Find thedistancefrom point Find thedistancefrompoint 1 A 1 100 For usewiththelesson“ProveTheoremsaboutPerpendicularLines” Practice A mapofaneighborhoodisdrawn where onagraph unitsaremeasured a m m y b 1 2 63 300 1. 2. 8 c 500 c x d

P 700 900 continued e 23. P P

toline toline 1 A y 1 c a . Roundyour answer tothenearestfoot. . c x

24. Date

———————————— A 1 y 1 Practice Workbook c Geometry x 57 58

sides. Thendetermineifitisarighttriangle. A trianglehasthegivenvertices.Graphandclassifyitbyits Classify thetrianglebyitssidesandangles. Complete thesentencewith Name 8. 5. 4. 3. 2. 1. Practice Workbook Geometry LESSON

Arighttriangleis?anisoscelestriangle. Arighttriangleis?anequilateral triangle. Anobtusetriangleis?aright triangle. Anisoscelestriangleis?a right triangle. 4.1 A ——————————————————————— (3, 1), 2 y For usewiththelesson“ApplyTriangle SumProperties” Practice 100 2 B (3, 4), C (7, 1) x 6. always 9.

A (1, 1), , sometimes 2 y 2 B (4, 0), C , or (8, 5) x never

. 10. 7. Date

A 75 (2, 2), ———————————— 2 y 2 75 B (6, 2), C (4, 8) x

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Name Find themeasureofnumberedangle. Find themeasureofexteriorangleshown. Find thevalueof

22. 21. 17. 14. 11. 19. LESSON

In In 4.1 each angle. each angle. x ——————————————————————— 80

1 3 n n 20. (3 ABC ABC x For usewiththelesson“ApplyTriangle SumProperties” Practice 2 22) x , , m m

A A x x

. Thenclassifythetrianglebyitsangles. 5 5

2( m m B

continued B 1 ) and 30 18. 15. 12. 8 and m

(4 m C 2 x 4 2 x

5 C 3( 8)

5 m

3 m 51 x (2 B x ). Find themeasureof B

1 55 3) 60 8 16.

. Find themeasureof 13. Date

(103 50 2 ———————————— x 20 x ) 1 x Practice Workbook (6 3 2 x 58 22 4 70 7) Geometry 59 60 Name Find thevaluesof 23. 26. Practice Workbook Geometry LESSON

4.1 the triangleby itsangles. byformed itssides. Then copy thetriangle,measureangles,andclassify andhorizontalwoodenstrengthening avertical junction.Classifythetriangle Metal Brace ——————————————————————— 10.5 in. y x 7.7 in. For usewiththelesson“ApplyTriangle SumProperties” Practice The diagram shows Thediagram thedimensionsof a metalbraceusedfor 30 7.14 in. x

and y . continued 24.

x 56 y 50 39 25. Date

74 70 ———————————— x y 78

Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Name Find thevalueof congruent. Write acongruencestatementforanyfiguresthatcanbeproved 2. In thediagram, 1.

11. 8. 6. 4. LESSON trianglesshown Copy thecongruent atright. 4.2

G E D E corresponding angles and corresponding sides. anglesandcorresponding corresponding n ofyourThen labelthevertices trianglessothat MT m D ——————————————————————— A

P AMT

M 5 ù

? ? 5 For usewiththelesson“ApplyCongruenceandTriangles” Practice

> Explain ?

n CDN n TJM x . yourreasoning. . Identify all pairs of congruent . Identifyallpairsofcongruent x

> F

65 n

F PHS C B

12. . Completethestatement. 7. 5. 3. 9.

JM PM } n m HPS

ù P N ?

T 5

ù ? ? R

70 A 10. Date

E B F

Y T X Z

M 73 ———————————— J 2 x S

48 60 5 cm D Practice Workbook H Geometry P

W 61 62 Name values of values of indicated values. In Exercises13and14,usethegiveninformationtoﬁnd 14. 13. 15. Practice Workbook Geometry LESSON Given Given 4.2 Graph the triangle with vertices Graph thetrianglewithvertices to and ——————————————————————— n C ABC (5, 4). Then graph a triangle congruent (5, 4). atrianglecongruent Then graph n n For usewiththelesson“ApplyCongruenceandTriangles” Practice HJK ABC a x . and and

ù ù y b

. n . n TRS DEF , ﬁndthe , ﬁndthe continued A

(1, 2), B (7, 2),

A D 87 H 2 3 51 y y C F 2 B E (7 J b 42

Date 10) S T ———————————— (5 K x (6 x 83 R a

Statements

17. 16. LESSON 4.2 PROVE: GIVEN: triangles arecongruent? used tomake allofthetrianglesindesign. guaranteesthatallthe Which property Carpet Designs 4. 3. 2. 1. Proof ——————————————————————— ? n BD } AD }

ABD ABD Completetheproof.

ù ù For usewiththelesson“ApplyCongruenceandTriangles” Practice

BD } BC } AD }

ù ù

ABD ABD

n ù AB } CDB CDB

A carpet is made of congruent triangles. Onetriangularshapeis ismadeof congruent Acarpet BC }

ù ù ù

DC } , n

AB } CDB CDB

ADB ù continued

DC } , ù

ADB

CBD ù

, CBD ,

Reasons 3. 2. 1. 4. ThirdAnglesTheorem ? Given ? D A B Date ———————————— C Practice Workbook

Geometry 63 Name ——————————————————————— Date ————————————

LESSON Practice 4.3 For use with the lesson “Transformations and Congruence”

Identify the transformation you can use to move ﬁgure A onto ﬁgure B. 1. 2. 3. BA B B

A A

Copy the figure. Draw an example of the effect of the given transformation on the figure. 4. translation 5. reflection 6. rotation

Tell whether a rigid motion can move figure A onto figure B. If so, describe the transformation(s) that you can use. If not, explain why the figures are not congruent. 7. y 8. y 9. y

Geometry 64 Practice Workbook Name ——————————————————————— Date ————————————

LESSON Practice continued 4.3 For use with the lesson “Transformations and Congruence”

10. y 11. y 12. y A A B 1 1 1

1 x 1 x 1 x A B B

Designs for windows are shown below. Describe the rigid motion(s) that can be used to move ﬁgure A onto ﬁgure B.

13. 14. B AB

15. Clothing Design Mario created a metal chain belt with congruent links as shown. Describe a combination of transformations that can be used to move link A to link B.

Geometry Practice Workbook 65 Name ——————————————————————— Date ————————————

LESSON Practice continued 4.3 For use with the lesson “Transformations and Congruence”

16. Flags Kiley is designing a ﬂag for the school’s drill team, the Bolts. Describe the combination of transformations she used to create the ﬂag.

17. Toys A toy manufacturer wants to design a forklift truck similar to the one shown. Describe a combination of transformations that can be used to move part A to part B.

A B

Identify the type of rigid motion represented by the function notation. If the function notation does not represent a rigid motion, write none. 18. (x, y) n (x, 2y) 19. (x, y) n (2x, 2y)

Geometry 66 Practice Workbook Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Decide whethertheﬁgureisstable. Use thegivencoordinatestodetermineif Decide whetherthecongruencestatementistrue. Name

8. 1. 7. 6. 5. 4. LESSON

4.4

D A n A A A A ——————————————————————— ( (2, (1, 1), (1, 2), 2 ABD 3, 0), 2 2), For usewiththelesson“ProveTriangles CongruentbySSS” Practice

ù B B (4, 0), (4,

B B n (6, 2), (5, 1), CDB 2 3), C C B 2. C C C

(7, 5),

( (4, 8), (2, 5), 2 1, 9), D (4, D D (7, 5), (4, 7), D 2 (4, 9. 5), 2 E E E T n 10), S (6, (10, 8), (7, 2), RST Explain 2 E

(13, 6), ù F F

F (5, 10) n n (9, 13) 2 yourreasoning. (9, RQT ABC 8), 2 F

> (6,

Explain n 2 DEF 1) . 10. yourreasoning. 3. Date

A n ABC ————————————

C ù

n B F DEF Practice Workbook E D Geometry 67 68 Name

Determine whether

Statements 11. 13. Practice Workbook Geometry LESSON

4.4 A C GIVEN: PROVE: 4. 3. 2. 1. Proof ———————————————————————

n AC AC } BC } AB } ABC

Completetheproof.

ù ù ù 10 For usewiththelesson“ProveTriangles CongruentbySSS” Practice 8

AC AC } CD } AD } AB } n

ABC

n ù F 2 E

CDA B 2 CD }

ù n ,

n ABC BC } 8 10 CDA

continued >

AD }

n D

12. DEF . Explain yourreasoning.

A Reasons 4. 3. 2. 1. A ? ? ? ? 5 7 B F 1 E B C 2 5 Date 7 D ————————————

D C

Statements 15. 14. LESSON

4.4 Picture Frame GIVEN: Which pictureframeisstable? PROVE: 5. 4. 3. 2. 1. Proof ———————————————————————

n BD } AD } D AB } ABD is themidpointof

Completetheproof.

ù ù ù For usewiththelesson“ProveTriangles CongruentbySSS” Practice

CB } BD } CD } AB } n

ABD

ù n Thebacksoftwo different pictureframesareshown below.

CBD CB }

ù ,

n D

CBD is themidpointof AC . AC } continued

Explain your reasoning. AC . AC }

Reasons 5. 4. 3. 2. 1. A ? ? ? ? ? D B Date ———————————— C

Practice Workbook Geometry 69 70 postulate ortheoremyouwoulduse. are congruent.Ifthereisenoughinformation,statethecongruence Decide whetherenoughinformationisgiventoprovethatthetriangles are congruentusingtheSASCongruencePostulate. Decide whetherenoughinformationisgiventoprovethatthetriangles 5. of sides. Use thediagramtonameincludedanglebetweengivenpair Name

10. 7. 3. 1. Practice Workbook Geometry LESSON

4.5 DA DA AB M A C F n n } } AB } T ——————————————————————— MAE ABC

and and

and A B E , For usewiththelesson“ProveTriangles CongruentbySASandHL” Practice , BD } AB } BC } n n DEF 6. TAE 4. 2.

11. 8.

CD BD BC M n n } } } A D DKA MNO and

and and

O , CD } DA DA } , DB } n n K SKT

RON

R 12.

S T

A D 9. Date

B T A n n JRM ABC ———————————— , , MR n n J JTM ADC D B C

using theindicatedpostulate. State thethirdcongruencethatmustbegiventoprove Statements

16. 15. 14. 13. LESSON

4.5 GIVEN: GIVEN: GIVEN: GIVEN: PROVE: Proof 6. 5. 4. 3. 2. 1. ——————————————————————— ? ? n B B is themidpointof is themidpointof ABD ABD Completetheproof. For usewiththelesson“ProveTriangles CongruentbySASandHL” Practice

Use the SSS Congruence Postulate.Use theSSSCongruence Use the HL Congruence Use theHLCongruence Theorem. Use the SAS Congruence Postulate.Use theSASCongruence RM } JR } JR } B B n

ù ù

is themidpointof is themidpointof J ABD

ù ù

n ù ù

EBC } DF DF } EBC

FB }

ù D , ,

JM } JM }

, ? EBC J AE CD } }

ù ù isarightangleand

continued . DB } DB }

. ù ? ,? ,?

CD } AE } .

ù ù ? ?

Reasons 6. 5. 4. 3. 2. 1.

? ? Deﬁnitionofmidpoint ? Deﬁnitionofmidpoint ? D R J M D A n Date B JRM ———————————— F

n E DFB C

B Practice Workbook

Geometry 71 72 Name

Statements 17. Practice Workbook Geometry LESSON 4.5 GIVEN: PROVE: 5. 4. 3. 2. 1. Proof ———————————————————————

n CB } AB } AB } ABC ABC

Completetheproof.

ù i ù For usewiththelesson“ProveTriangles CongruentbySASandHL” Practice CD }

CD }

CB } AB } n

ù ù

ABC

n i

CD } DCB DCB

ù , AB }

DCB

CD } continued

Reasons 5. 4. 3. 2. 1.

? ? ? ? ? C A Date ———————————— D B

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. postulate(s) ortheorem(s)youwoulduse. Is itpossibletoprovethatthetrianglesare congruent? Ifso,statethe using thegivenpostulateortheorem. State thethirdcongruencethatisneededtoprove State thethirdcongruencethatisneededtoprove Name using thegivenpostulateortheorem. 7. 2. 1. 6. 5. 4. 3. LESSON

4.6 W GIVEN: GIVEN: GIVEN: GIVEN: GIVEN: GIVEN: ———————————————————————

For usewiththelesson“ProveTriangles CongruentbyASAandAAS” Practice

Use the AAS Congruence Theorem. Use the Postulate.ASA Congruence FE } Use the AAS Congruence Theorem. BC } DF } DE } Use the Postulate.ASA Congruence Use the AAS Congruence Theorem. Use the SAS Congruence Postulate.Use theSASCongruence

A A

> > > > >

ON }

YZ } MO } MN } L

X ,

, ,

, , Y AB } F C F

F B

> > >

XY }

Z O Y O , ?

, ? D 8. , ? , ? , ? , ? T

> > > > > > ? ? ? ? ? ? H N S

D B A n n DEF ABC U E 9. F Date M C Y

K >

X n ———————————— MNO XYZ N O

Practice Workbook H N G Geometry L

73 74 Name using thegivenpostulateortheorem. Explain howyoucanprovethattheindicatedtrianglesarecongruent n Tell whetheryoucanusethegiveninformationto determinewhether

16. 15. 14. 12. 10. JRM Practice Workbook Geometry LESSON

4.6 n n n JM } ———————————————————————

BEF AFB ADB > J

> >

XZ }

XYZ

> For usewiththelesson“ProveTriangles CongruentbyASAandAAS” Practice > > X

n n n , BED . CDB CFB M Explain M

by SAS > by AAS by ASA

Z Z , yourreasoning. ,

R continued R

Y Y

13. 11.

JM A } F E D M

XZ }

Z JR } ,

> R Date

XY }

, ———————————— B Y J ,

> JM }

> X

XY }

Statements

18. 17. LESSON

4.6 GIVEN: PROVE: Proof GIVEN: 6. 5. 4. 3. 2. 1. Proof PROVE: ———————————————————————

n WX } WU } XU } WXU

UXW UWX Writeaproof. Completetheproof.

> i For usewiththelesson“ProveTriangles CongruentbyASAandAAS” Practice i

ZV }

YV }

WU } YZ } n n

> > >

WXU

B ABC

ù i

YZV YV } VZY VYZ

ù > ,

XU }

n , EDC AC AC } YZV

V , ZV , } ù continued

WX } DC }

YZ }

Z A Reasons 6. 5. 4. 3. 2. 1.

? ? ? ? ? ? V U B C D Date Y E X ———————————— Practice Workbook W Geometry 75 76

Use thediagramtowriteaplanforproof. statement. Whatpostulateortheoremwouldyouuse? Tell whichtrianglesyoucanshowarecongruent in ordertoprovethe Name

7. 4. 1. Practice Workbook Geometry LESSON

4.7 A N G H T H N G PROVE: BC } A K M ——————————————————————— B

KHN

AD }

For usewiththelesson“UseCongruentTriangles” Practice > I

2. DAB MGT B D D

C ù 5.

BCD

T BD } D A E

TSU

BE }

6. VSU B 8. U S

3. P PROVE: R C S

ST }

V ù

Date

RQ } BC C A } Q

ADB

———————————— ù A T

AT } B

CBD D B T C

Statements Explain 5. Use theverticesof

11. 10. 9. LESSON

4.7 GIVEN: Proof A A PROVE: 6. 4. 3. 2. 1. ——————————————————————— (2, 3), (1, 2),

} XZ } ZX } YX } YZ n yourreasoning.

YXZ YXZ

bisects Completetheproof. ù ù ù For usewiththelesson“UseCongruentTriangles” Practice B B

} WZ

XZ } WX }

ZX } YX } (2, 9), (4, ù ù

YZ }

bisects n

2 ù ù

WXZ WXZ 3),

C WX } YXW WZ } n C (6, 6),

ABC (2, 5), .

YXW D and continued (8, 5), D . (4, 7), n

E DEF (8, 11), E (7, 2), toshowthat F F (12, 8) (5, 10)

Y Reasons 6. 5. 4. 3. 2. 1. W ? ? ? ? ? ? A

Z X O D . Date ———————————— Practice Workbook Geometry 77 78 Name

Use theinformationgivenindiagramtowriteaproof. 12. Practice Workbook Geometry LESSON

4.7 N PROVE: ——————————————————————— For usewiththelesson“UseCongruentTriangles” Practice M

MN }

TQ } 13. T continued Q

D PROVE: A

DB }

ù Date

CB } B

———————————— E C

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. are congruent. Decide whetherenoughinformationisgiventoprovethatthetriangles Find thevaluesof Name 7. 1. 4. LESSON

4.8 B 4 A ——————————————————————— y (3 x (5

2 x 11) For usewiththelesson“UseIsoscelesandEquilateralTriangles” Practice (3 x 10) 2 Explain y 10) (2 x x

D C

and 1

11) youranswer. y .

5. 2. (2 x 3

x 11) 142 8. ( x

( y 2)

y L 1 7)

6. 3. Date P 8 (2 ( x x ————————————

3 y

25) 5) ( x (9 (4

2 y x

2) Practice Workbook

1 28) 10) Geometry 79 80 Name Statements In Exercises9and10,completetheproof. Statements 10. 9. Practice Workbook Geometry LESSON

4.8 GIVEN: GIVEN: 6. 5. 4. 3. 2. 1. PROVE: 5. 4. 3. 2. 1. PROVE: ——————————————————————— ? ? ? AE } AC } HF } HG } FG } 3 AEC 1

> > > > > > > For usewiththelesson“UseIsoscelesandEquilateralTriangles” Practice

BD } BE }

IF } FJ }

IJ }

FG } HF } >

4 2

> > > > BED

FJ } IF } 2, , ,

HG } AC }

> > continued

IJ } BD } 6. 4. 3. 1. 4. 2. 5. 1. 2. Reasons Reasons 5. 3.

? Theorem Congruence AAS ? ? Postulate SASCongruence Base Angles Theorem ? ? ? ? ?

G H I J I G H C Date A B 1 3 ———————————— E F 4 2 D

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Name vertex angles. wheel stopson. areisoscelestriangleswithcongruent The 9trianglesinthediagram station. People spinthewheel andreceive tothenumber theprizethatcorresponds Prize Wheel In Exercises17–19,usethefollowinginformation. theorem youused. In Exercises11–16,usethediagram.Completestatement.Tell what

19. 18. 17. 16. 15. 14. 13. 12. 11. LESSON If If If If If If Trace theprizewheel. atriangle Then form Explainhow you know thattriangle1is Themeasureofthevertex angleoftriangle1 4.8 triangle isthis? of thetriangles1,4,and7. What typeof whose arethemidpoints ofthebases vertices totriangle6. congruent is40 ——————————————————————— TP } RP } PQ } PUV PSQ PQV

> > > . Find themeasuresofbaseangles. Aradiostationsetsupaprizewheel when they areoutpromotingtheir For usewiththelesson“UseIsoscelesandEquilateralTriangles” Practice

TR } SP } PT }

> > > , then , , then ,

, then ,

SPQ PVU PVQ , then? , then? , then? ? ? ? > > > continued

?. ?. ? . ?. > > > ?. ?. ?.

Q 8 7 9 V Date 6 RS 1 ———————————— 5 P 2 4 3

Practice Workbook U Geometry T 81 82

thetranslation( thetranslation( Sketch Sketch

6. Name thetypeoftransformationshown. Name 4. 1. Practice Workbook Geometry LESSON

4.9 B B Figure Figure ——————————————————————— (4, (6, 2 2 3 3 3), 2), ABCD ABCD For usewiththelesson“PerformCongruenceTransformations” Practice ABCD ABCD y y 1 C C 3 3 y (5, 5),and (5, 3),and 1 has vertices hasvertices hasvertices adda t mg fe Sketch anddraw itsimageafter Sketch anddraw itsimageafter x x , , y y ) ) m m x x x

D D ( ( x x 4 ) (4, 7). 0 ) (0, 4). 2 1 A A (3, (1, 2), 3, 5, 2. y y 2 1 1

1), 2. thetranslation ( 2). 3. thetranslation( 3). 2 y 2 5. 7.

B B Figure Figure (1, 7), (4, x 2 3. 3 3 1), ABCD ABCD ABCD ABCD C y y (6, 2),and C 3 3 (6, 4),and has vertices hasvertices has vertices hasvertices anddraw itsimageafter anddraw itsimageafter Date

x x , , y y ) ) ———————————— m m x x D ( D ( ( 2 2 x x (1, 5). 1, 1 2 A A y 2 ( ( 4, 2, 2 2 2). 2, 3), 1, 3), y y 2 2 6 5). 4). x

AB } Use thecoordinatestograph Use areﬂectioninthe 8. Use coordinatenotationtodescribethetranslation. 15. 12. 10. LESSON abouttheorigin.Ifso,giveangleanddirectionofrotation.

4unitstotheleft,6up

4.9 A 3 unitstotheright,5down ——————————————————————— ( 2 2, 5), For usewiththelesson“PerformCongruenceTransformations” Practice 1 2 B ( y y 2 1 2 2, 0), C x x y

(0, 1), -axis todrawtheotherhalfofﬁgure. continued D 13. AB } (3, 1)

and 16. CD } .Tell whether

8 11. y 9. 2 1unittotheright,8unitsup 7unitstotheleft,2down

A (1, 4), x 14. 2 CD } B y (4, 1), 2 isarotationof

Date

C (1, ———————————— x 2 4), D 8 (4, y 2 Practice Workbook 2 1) Geometry x 83 84 Name corresponding pointontheoriginalﬁgure. A pointonanimageandthetransformationaregiven.Find description, points(2,0)and(3,4)aretwoverticesofatriangle. Complete thestatementusingdescriptionoftranslation.In 17. 21. 20. 19. 18. Practice Workbook Geometry LESSON If(2,0)translatesto(4,1),then (3,4)translatesto?. 4.9 of n Verifying Congruence Point onimage:( Point onimage:(2, If (2,0)translatesto( ——————————————————————— DEF n ABC is a congruence transformation transformation isacongruence For usewiththelesson“PerformCongruenceTransformations” Practice . Explain 2 your reasoning. 5, 2 2 ( 4); transformation: 2 Verify that 7); transformation: ( 7); transformation: 2, continued 2 1), then(3,4)translatesto?. x , x y , ) y m ) m ( x ( 2 x

, 4, 2 1 y y ) A y 1 1 B 3) D Date C E ———————————— F x

Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. coordinates toeachvertex. Place thefigureinacoordinateplaneconvenientway. Assign In DE } Name the statement. 12. 11. 10. 13. 4. 1. 9. 8. 7. 6. 5. n isamidsegmentof LESSON

Rectangle:lengthis7unitsandwidth4 Righttriangle:leg lengthsare5unitsand3

5.1 JKL A JR } SL } KL } ST } RS } Isosceles righttriangle:leg lengthis12units Square: sidelengthis6units JT } ———————————————————————

> > > i i i , ?

x ? ? ? JR } ? ? For usewiththelesson“MidsegmentTheoremandCoordinateProof” Practice

E > B 7

> > >

RK } ? ? ? D , KS } C

> n

SL }

ABC ,and

. Findthevalueof 2.

JT } A J

TL } x

.Copyandcomplete D E R 8 B x . T C

K 3. S Date

A D L ———————————— B x 34 E Practice Workbook C Geometry 85 86 Name

the givenstatementistrue. Find theunknowncoordinatesofpoint(s)inﬁgure.Thenshowthat Use

17. 16. 15. 19. 14. Practice Workbook Geometry LESSON Thecoordinatesof If 5.1 n formed byformed connectingthethreemidsegments of of eachsideandtheperimeter n If If B ———————————————————————

GHJ (?, ?) HJ EF DE ABC

5 5 5 , where (

For usewiththelesson“MidsegmentTheoremandCoordinateProof” Practice 2 > 8 2 4 h C x

x x , 0) n (0,

2 1 1 DEC 2and 7and k 5and ) D

, n E DF GH GJ , and ABC

5 5 E D 5 ( continued ( 2 3 are h 5 h F , , 2 x x x k aremidpointsofthesides.

1 1 ) 2 k A ) 11,what is 25,what is (0, 5), 1,what is

n ABC B (8, 20),and . Then ﬁndtheperimeteroftriangle EF HJ DE ? 18. ? ? n

ABC PT } C S P

(0, 26).Find thelength (0, 0) (?, ?) .

G > D

SR } H

Date ( F h , k ) E ———————————— T R (?, ?) (2 h , 0) J

Name 21. 20. LESSON

5.1 is assembled? will thebottomsoflegs bewhen theframe legs. At eachendoftheframe,how apart far You attachthecrossbarsatmidpointsof the kityou purchasedareeach36incheslong. for aswing set. The horizontalcrossbarsin Swing Set A-Frame House the floorofsecondlevel, labeled Explain 20 feetlong?2430 can is closertothefirstfloor, midsegment ——————————————————————— LM } For usewiththelesson“MidsegmentTheoremandCoordinateProof” Practice be12feetlong?14

. You areassembling theframe JK } Explain

. If Inan A-frame house, JK } is14feetlong, . NP } continued , thanisthe

LM }

, N L e leg leg J crossbar ? Date ———————————— K

M Practice Workbook P

Geometry 87 88 indicated measure. Use thediagram. is ontheperpendicularbisectorof Tell whethertheinformationindiagramallowsyoutoconcludethat Find thelengthof Name

11. 9. 7. 4. 1. Practice Workbook Geometry LESSON Find Find Find 5.2 AC A ——————————————————————— 2 FH FG EF x For usewiththelesson“UsePerpendicularBisectors” Practice . . . C D B EH } AB } 5 B x istheperpendicularbisectorof

. 2 12. 10. 8.

Find Find Find 2. DF DG DE . . . 5. D C AB } A C .

7 3 A B x x 2 1

16 8 3

7 1 x 4

1 DF } y B 9 E F

.Findthe 7 3. 9 y x

Date 1

2 H 11 6 8 6. 1 x B x A 1 ———————————— G 2

9 10 D y A

C 2 C E 4 C

B D

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Name C choose point Draw are showndashed.Findtheindicatedmeasure. In thediagram,perpendicularbisectorsof

17. 15. 13. 19. and LESSON Find Find 5.2 Find AB ——————————————————————— AB } AB }

withthegivenlength.Constructperpendicularbisectorand CF AG CE

is1inch.Measure 0.5inch For usewiththelesson“UsePerpendicularBisectors” Practice . . . 18. C ontheperpendicularbisectorsothatdistancebetween 16. 14. Find Find continued Find AC } 20. BG BD AC and

. . . AB BC }

5 1inch .

A ABC 20 meetatpoint 24 D 21. G F Date

AB B ————————————

5 25 15 G 2inches and E C Practice Workbook Geometry 89 90 Name Write atwo-columnorparagraphproof.

22. 24. Practice Workbook Geometry LESSON

5.2 the endsofwires? the same. What doesthattellyou aboutthepostandsectionofframebetween same anddistancesfromthebottomofposttoendstwo wiresare The lengthsofthewiresfromtopaposttoedgesframeare posts totheedgesofwings,which were wooden framescovered withcloth. Set Early Aircraft GIVEN: PROVE: A ——————————————————————— For usewiththelesson“UsePerpendicularBisectors” Practice

bisector of CD } n D C ACD is the perpendicular istheperpendicular

> On many of the earliest airplanes, wires connected vertical wiresconnectedvertical Onmany oftheearliestairplanes,

n B AB }

BCD . continued

23.

EH GIVEN: PROVE:

n EF } GHJ

J > F G Date

EG }

n ———————————— FHJ

Find thevalueof Can youconcludethat Use theinformationindiagramtoﬁndmeasure. Name 7. 4. 1. LESSON

Find

5.3 B B (4 (5 ——————————————————————— x x A 5) 2) AD For usewiththelesson“UseAngleBisectorsofTriangles” Practice A C C D . 19 D x .

BD # ### $

bisects 8. 5. 2.

Find ABC m H D ? 6 6 EFH 8 4 Explain E A x G C x 28 9 3 . 8

. F B

3. 9. 6. Date

Find 6 x 3 J ————————————

x 2

m 1 17 7 D 7 JKL K A C M 43 . Practice Workbook 8 7 L B Geometry 91 92 Name

Find thevalueof Find theindicatedmeasure. Can youﬁndthevalueof Find 15. 10. 13. Practice Workbook Geometry LESSON

5.3 K A Point ——————————————————————— A B B BG G M 34 N For usewiththelesson“UseAngleBisectorsofTriangles” Practice 4 istheincenterof . Find x 9 x 16 L 52 C FE G 48 x thatmakes C D

x n continued ? ACE Explain 11. N .

theincenteroftriangle. . 34 14. 16. x 8 8

Point

D H 12. J JP P istheincenterof . K P N L 25 Date

24 K 3 x N ———————————— x M 41 8 E 8 n M 51 L HKM 45 F .

18. 17. LESSON

5.3 B your friendfromscoringagoal? (point goalpost The goalextends fromleftgoalpost friend isgoingtoshootthepuckfrompoint your driveway. You arethegoalie,andyour incenter monument tobethesamedistancefromeachedgeofpark.Useﬁgurewith Monument Hockey ——————————————————————— G For usewiththelesson“UseAngleBisectorsofTriangles” Practice You andafriendareplaying hockey in ) tohave thebestchancetoprevent G R 120 ft to determine how todetermine frompoint far . Where shouldyou positionyourself You arebuildingamonumentintriangularpark. You want the 125 ft FE G A DC continued Explain. L toright D S . you shouldbuildthemonument.

L Goal G S Date R

———————————— Practice Workbook Geometry 93 94 Is Find thecoordinatesofcentroid 1. length ofthesegment. G Name

10. 8. 7. 5. 3. isthecentroidof Practice Workbook Geometry BD } LESSON shown. Usethegraph 5.4 b. AC A CG } EG } BD } a. a ——————————————————————— ( Find thecoordinatesof 2

perpendicular bisector

Verify that Find thecoordinatesof Use themedian of thecentroid 7, 2 For usewiththelesson“UseMediansandAltitudes” Practice D B 4), B ( 2 KP 3, 5),

n 5 P LM } .

ABC } 3 2 6. 4. 2.

C KN. toﬁndthecoordinates

(1, , DG } AE } AB } N M AD 2 , themidpointof , themidpointof

11. of

8, n A

ABC AG P B of

D 5 ? Is 10,and n JL }

ABC JK BD } } 9. . . a

. A A median 8 (0, CD D C 2 12.

5 2), 10 B 18.Findthe ? an J B ( G (6, 1), 2 F 2, 7) Date altitude

A E 2 C 2 (9, ———————————— y B 2 2 L C ? (2, 5) D K 2 (6, 1) 5) x C

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Complete thesentencewith value of Point Copy andcompletethestatementfor Find themeasurements. Name

and 20. 19. 18. 15. 14. 13. 24. 23. 22. 21. LESSON Given that 5.4 KM } BG CG PN FG Given that The altitudesofatriangle ?intersectinsidethetriangle. The mediansofatriangle?intersectinsidethetriangle. bisector.The altitudeofatriangleis?theperpendicular bisector.The medianofatriangleis?theperpendicular ——————————————————————— G

isthecentroidof

,andcentroid

5 5 5 5 x ? 5

. 3 x For usewiththelesson“UseMediansandAltitudes” Practice

x x 1

2 1 8and G AB 1and 7and HN isthecentroidof 5

AF BC, DG CE

5 P ﬁnd

5 . 5 9 6 4 x n

continued AD x 2 x

ABC 2 6 always 16. and 5 n ABC . Usethegiveninformationtoﬁnd

m PL , , ﬁnd

ABC. sometimes 5 n ? HJK FG and JP withmedians

BD , or

. never A

E . 17. HN } AD Date

B , G KP JL } D ————————————

5 E 13 ? F 10 KM B G Practice Workbook C 39 12 8 Geometry F C 95 96 Name

26. 25. Practice Workbook Geometry LESSON

5.4 Art ProjectArt House Decoration Find thealtitude. Will thetrianglefitinyourpiece? art the height(altitude)mustbelessthan8.5millimeters. dimensions shown. Inorderforthetriangletofit, You want anisoscelestrianglewiththe toinsert consists ofdifferent items ofallshapesandsizes. should you placethedecoration? to point of thetriangle. You measurethedistancefrompoint door. You want toplacethedecorationoncentroid on your houseinthetriangularareaabove thefront ——————————————————————— For usewiththelesson“UseMediansandAltitudes” Practice B (seefigure).How down far frompoint You piecewhich aremakinganart You aregoingtoputadecoration continued Explain .

10 mm Date 12 mm A B ———————————— 54 in. 10 mm

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. List thesidesandanglesinorderfromsmallesttolargest. side inblue.Whatdoyounotice? largest angleandlongestsideinredthesmallestshortest Use arulerandprotractortodrawthegiventypeoftriangle.Mark Name 1. 8. 6. 4. LESSON

5.5 X D AC Obtuse scalene Y ——————————————————————— 8 426 24 45 F 98 8 8 B For usewiththelesson“UseInequalitiesinaTriangle” Practice 22 10 14 37 8 9. Z E 5. 7. 2. Acute isosceles P 25 K J R S 58 8 18 17 R T 60 3. 32 8 Date 8 Right isosceles L ———————————— Practice Workbook Geometry 97 98 Name

the anglemeasuresoftrianglefromleast togreatest. Is itpossibletobuildatriangleusingthegiven sidelengths?Ifso,order lengths oftheothertwosides. Describe explain Is itpossibletoconstructatrianglewiththegivensidelengths?Ifnot, Sketch andlabelthetriangledescribed. Anglemeasures:42 Anglemeasures:45 25. 16. 13. 22. 19. 12. 11. 10. Practice Workbook Geometry LESSON 22,26,65 3,4,5 sideonthebottom Sidelengths:11,18,and24,with shortest 5.5 RS 21 yd, 16yd 6 in.,9in. vertically attheright. sidearranged Side lengths:32,34,and48,withshortest Angle measures:25 Side lengths:14,17,and19,withlongestsideonthebottom ——————————————————————— whynot. 5 thepossiblelengthsofthirdsidetrianglegiven

Ï For usewiththelesson“UseInequalitiesinaTriangle” Practice } 46 ,

5 3 Ï 8 8 8 } 5 , , 45 , 60 , 44

RT 8 8 8 , and93 , and75 , and111 continued

5 5 23. 20. 17. 14. 8 8 22in.,2ft 4ft,12ft 6,43,39 1,4,6 , withlargest angleatthetop. , withsmallestangleattheright 8 , withlargest angleattheleft 26.

Ï } 26 ,

24. 21. 18. 15. BC Date 24in.,1yd 9m,18m 7,54,45 17,33 5 4 Ï ———————————— } 5 ,

5 2 Ï } 2

Baseball Airplanes 5.5 A relationships thatwould leadtothisconclusion. the closesttoperson boat anglerelationshipstoconcludethat certain in thewater. Talking by radio, thecaptainsuse positions oftwo rescueboatsandtwo people Sea Rescue the shortest andlongestpossiblethe shortest distances. Explain why the Triangle Inequality Theorem can beusedtodescribeallbut What canyouabout how determine theballlandsfrompitcher’s far mound? plate. A batter pops theballupanditcomesdown just24feetfromhomeplate. two canbeatthistime. airplanes 640 miles. hastraveledAfter 2hours,oneairplane 710miles andtheotherhastraveled Building What canyou say about theheightofbuilding? top ofthebuildingis51 building. The angleofelevation fromyour feettothe ——————————————————————— thepossiblevaluesof A istheclosesttoperson 5 For usewiththelesson“UseInequalitiesinaTriangle” Practice You arestanding200feetfromatall A pitcherthrows abaseball60feetfromthe pitcher’s moundtohome Describe Two leaveheadingindifferent directions. airplanes thesameairport Theﬁgureshows therelative 7 B 2 therangeofdistancesthatrepresentshow the apart far x D

2 . C 8 Describe 2 (asshown intheﬁgure). continued

C andboat x theangle . B is 28.

4 x A

1 18 2 Date C ———————————— 200 ft D 8 G B 51 Practice Workbook 8 Geometry you

99 100

Complete with<,>,or Name 7. 5. 3. 1. Practice Workbook Geometry LESSON

5.6 J RTUW m m JK ST 17 ——————————————————————— 2 ? ? 54 1 1

? ? 8 2 For usewiththelesson“InequalitiesinTwo Triangles andIndirectProof” Practice S 29 18 VW LM K 55 m 18 m 4. 2. 1 59 8 M 30 2 2 8 8. 6. 16 52

8 1 5 V

Explain. L

D m DE AB m 29 B 61 A ? 1 ? 1

? ? 9 1 98 CD EF E 8 12 m E m G 2 100 2 9 Date 2 8 D 31 ———————————— C F 60

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Name conclusion indirectly. Write atemporaryassumptionyoucouldmaketoprovethe 9. and solveaninequalitytodescribearestrictiononthevalueof Use theHingeTheoremoritsconverseandpropertiesoftrianglestowrite

13. 12. 11. LESSON Iftwo parallellinesarecutby atransversal sothatapairofconsecutive interior Iftwo linesinaplaneareparallel,thenthetwo linesdonotcontaintwo sides

5.6 b. angles is congruent, then the transversal is perpendicular totheparallellines. thenthetransversal isperpendicular angles iscongruent, of atriangle. Table Making top sothatthemeasureof identical measurements,butthey areattachedtothetable 36 a. ——————————————————————— Usethe Converse oftheHinge Theorem to Usethe Hinge Theorem to not level. table level. to determine whento determine 39 ( For usewiththelesson“InequalitiesinTwo Triangles andIndirectProof” Practice x

1 45 18) 52 8 Allfourlegs ofthetable shown have 8 45 10. 4 continued > 3 issmallerthanthemeasureof

explain 2 inreattachingtherearpairoflegs tomake the why thetable topis explain

how tousealengthmeasure 12 x 126 18 3 1. x 21

8 2 8 8 12 Date 18 x . ———————————— 2 1 Practice Workbook 4 3 Geometry

101 102 Name

F. E. D. C. B. 16. 15. 14. Practice Workbook Geometry LESSON

5.6 A. Write anindirectproofforCase2. Indirect Proof PROVE: of Case1. Indirect Proof the day? spend therestofday. pointattheendof fromthestarting Which anglerisfarther point,thengoesanother1.8milesinadirection84 the starting due eastfortherestofday. out1.2milesdueeastof A secondcontestant starts point,thengoes1.2miles ofthestarting atalocation1.8milesduenorth morning Fishing Contest Case 1: GIVEN: ——————————————————————— Because Temporarily assumethat Butthiscontradictsthegiven statementthat Thiscontradictionshows assumptionthat thatthetemporary Then Then reﬂexive property. For usewiththelesson“InequalitiesinTwo Triangles andIndirectProof” Practice Explain

m BD }

AB AD } AD } ADB

= > ADB isamedianof Thereare two casestoconsiderfortheproofinExercise 15.

AC isamedianof CD } Arrange statements Arrange A–F inordertowriteanindirectproof how you know. Onecontestantinacatch-and-releaseﬁshingcontestspendsthe

> <

by thedeﬁnitionofmidpoint. Also,

m ADC ADC continued AB n by theconverse oftheHinge Theorem. n ABC < ABC AC . . , D isthemidpointof ADB

> C AD }

> BC } ADC

AD } 8 southofdueeastto .

AB .

D A by the < Date AC ———————————— isfalse. B

statement andﬁndthescalefactor. Determine whetherthepolygonsaresimilar. Iftheyare,writeasimilarity the correspondingsidesinastatementofproportionality. List allpairsofcongruentanglesfortheﬁgures.Thenwriteratios Name 1. 4. 3. LESSON

6.1 B C F E E A. Multiple Choice n not correct? ——————————————————————— ABC 55 }

DE AB 34 A

D For usewiththelesson“UseSimilarPolygons” Practice

5 ,

} BC EF n DFE

B Triangles 2. 66 D ABC B. A

} FD CA and C F

5 DEF } DE AB

aresimilar. Which statementis 5.

N WXYZ 6416 4 16 W Z C. Z ,

MNOP O A W

> 4 C D

Date Y 24 24 F 6 6 ———————————— M A B X Practice Workbook P

Y X Geometry 103 104 side of 10 inches,14and20thelengthofanaltitudeis6.5inches. The shortest Similar Triangles In Exercises13and14,usethefollowinginformation. The twotrianglesaresimilar. Findthevaluesofvariables. In thediagram, Name

15. 14. 13. 11. 10. 9. 8. 7. 6. Practice Workbook Geometry LESSON altitudein Find thelengthofcorresponding Find thelengthsofothertwo sidesof Find theratioofperimeter Find theperimeterof Find theperimeterof Find thevalues of Find of thescalefactor 6.1 n A. the perimeterof of similar Multiple Choice ——————————————————————— n n WXY 18 inches 5.5 ABC For usewiththelesson“UseSimilarPolygons” Practice n 6 is15incheslong. DEF ? Triangles WXYZ i 3. The perimeterof : is4 WXYZ Theratioofone sideof x ,

y , MNOP WXYZ , and .

WXYZ RST MNOP continued 12 z and . m . B. . to . 24 inches WXY MNOP MNOP aresimilar. The sidelengthsof n . to n 8 DEF n

WXY ABC 12. is24inches. What is theperimeter n . to the corresponding sideofa tothecorresponding WXY

. Z C. y 32 inches W 15 12 m Date 12 z 4 Y 8 n RST 8 ———————————— X are O m P 10 135 10 8 10 N M x

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. The poolis30feetwide. The fenceis50feetwideand100long. rectangular fenceforsunbathing. The shapeofthepoolissimilartofence. Swimming Pool usethefollowinginformation. In Exercises20–22, In thediagram, Name

22. 21. 20. 16. 19. 18. 17. LESSON Find andcomparetheareas ofbothtriangles. Find thelengthofaltitudeshown in Find theunknown sidelengthsofbothtriangles. Find of thescalefactor Find strictly theareareserved forsunbathing. Whatisthelengthofpool? ofthepooltofence? Whatisthescalefactor 6.1 ——————————————————————— For usewiththelesson“UseSimilarPolygons” Practice Thecommunityparkhasarectangularswimming poolenclosedby a n XYZ

n n MNP XYZ continued to . n MNP n . XYZ .

Z P 4 10 X 6 Date Y 5.8 ———————————— M Practice Workbook 9 Geometry N 105 106

center Draw anexampleofthegivensimilaritytransformationfigurewith figure AontoB. The twofiguresaresimilar. Describethetransformation(s)thatmove Describe thedilationthatmovesfigureAontoB. Name 7. 4. 1. Practice Workbook Geometry LESSON dilation 6.2 P ——————————————————————— O . B For usewiththelesson“Transformations andSimilarity” Practice 12 P 10 A 17 B A 12 O

8. 5. 2. dilationthentranslation 5 O 18 A A 3 B P B 8 O

3. 9. 6. Date dilationthenrotation Q O ———————————— B Q 010 30 A 20 16 P B A

Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Describe thetransformationsthatmovefirstfigureontosecond. Coordinates oftheverticesapreimageandimagefigurearegiven. the dilation. the transformationinvolvesadilation.Ifso,givescalefactorof Figure BistheimageoffigureAunderatransformation.Tell whether Name 13. 17 16 15 14 10. . . . . LESSON

6.2 O J A O A ——————————————————————— ( ( ( (0, 0), (0, 0), 2 2 2 16, 0), 8, 0), 4, 2), For usewiththelesson“Transformations andSimilarity” Practice M S B (0, 2), B B (0, 4), K (0, (2, 4), A 16 (0, 2 2 T N 10), (5, 0); 20), C (6, 0); 20 ( 2 O O

2, 5); (0, 0); O (0, 0); O (0, 0), continued (0, 0), P 11. P ( M 2 (4, 0), X ( 8, 4), F 2 (0, (0, 10), 8, 0), 2 30 Q Q 4), (0, 5), (4, 8), 010 20 N Y G (0, 10), ( (15, 0) 2 A O 10, 0) R (0, 0) ( 2 O 4, 10) (0, 0) B

12. Date 20 6 ———————————— 66 A 6 9 Practice Workbook 30 9 Geometry 9 B 9 107 108

circle are similarbyﬁndingacenterandscalefactor ofadilationthatmoves Circle BistheimageofcircleAunderatransformation. Provethecircles Name 20. 19. 18. Practice Workbook Geometry LESSON tangent 6.2 to be shown attheright.Hewants thelengthofsmallerﬂower petals Computers be usedtomove shape A ontoshapeB. thatcan right. Describeacombinationofthreetransformations as acraftsproject.Onedesignwithsimilarshapesisshown atthe Crafts of transformations thatcanbeusedtomoveof transformations petal A ontopetalB. 28 ——————————————————————— A ontocircle } 5 3

Gailcutsandgluessimilarshapesontoawooden board ofthelengthlarger petals. Describeacombination For usewiththelesson“Transformations andSimilarity” Practice 9 Cameron uses graphics software Cameronusesgraphics tocreatetheﬁgure B A B .

30 continued P 45º A O A 20 B B Q 21. concentric A B 64 Date ————————————

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. 9. similarity statement. Determine whetherthetrianglesaresimilar. Iftheyare,writea Use thediagramtocompletestatement. Name 3. 1. 7. 5. LESSON

6.3 L B x n A ———————————————————————

5 B ABC 85 ?

X > 8 ? 45 For usewiththelesson“ProveTriangles SimilarbyAA” Practice , Z 8 ? K J 50 8 43 8 85 X 6. 4. 2. 8 C

47 y } } 12 AB ? ?

8 Z

5 Y ?

} 8 ? } EF

} CA ?

10.

8. F C LM L 73 8 6 35 K J 8 8 A 16 x K B Date P M y 63 8 ———————————— D J 35 8 12 Practice Workbook N N E Geometry 109 110 Name Find thecoordinatesofpoint usethediagramatright. In Exercises18–21, In Exercises14–17,usethediagramatright. C. A. 21. 20. 19. 18. 17. 16. 15. 14. 13. 11. Practice Workbook Geometry LESSON Is Is Nametwo pairsofsimilartrianglesandwritea angles. Listthreepairsofcongruent 6.3 R ﬁnd thelengthof R R R R similarity statementforeach. Multiple Choice Q ——————————————————————— (0, 0), (0, 0), (0, 0), (0, 0), 85 P n n 45 3 8

} 28 AED 50 ACD 5 8

8 For usewiththelesson“ProveTriangles SimilarbyAA” Practice S S S S (0, 7), (0, 10), (0, 6), (0, 4),

> ,

n n EAB BCE T T T In the diagram attheright, Inthediagram S T ( ( ( BC } 2 2 2

( ? 2 ? 9, 0), 6, 0), 8, 0),

. 20, 0), continued X X X (0, 4), (0, 2), (0, 2), X Z (0, 6), D. B. sothat Z Z Z

} 6 20 ( ( ( 7 x x x Z

, , ,

( y y y x ) ) ) , y n ) RST 12.

n H G

RXZ

AB D . D 4 5 T C Date A 7 ———————————— K C E R

X S y E M N Z B

Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Name Flag Pole usethefollowing information. In Exercises23–25, A. as shown inthediagram. shadow. This scenarioresultsintwo similartriangles of hisshadow coincideswiththetipofflagpole’s pole, a5foottallmalestudentstandssothatthetip 25. 24. 23. 22. LESSON Why arethetwo overlapping trianglessimilar? Whatistheheight Usingthesimilartriangles,writeaproportion 6.3 Multiple Choice that modelsthesituation. triangle. Which ofthefollowing isfalse? AB } ———————————————————————

and Inordertoestimatetheheight A For usewiththelesson“ProveTriangles SimilarbyAA” Practice

BC } >

arethelegs oftheﬁrsttriangle. D

Triangles h (infeet)oftheﬂagpole? continued ABC B.

AC and

h 5 ofaﬂag DEF

arerighttrianglesthatsimilar. DE }

and

EF }

arethelegs ofthesecond C.

A } DF AC

5 6 ft C }

Date DE AB B

5 ft ———————————— 12 ft Practice Workbook D E h Geometry

111 112 5. a similaritystatementandﬁndthescalefactorof Determine whetherthetwotrianglesaresimilar. Iftheyaresimilar, write Is either Name 1. 3. 2. Practice Workbook Geometry LESSON

6.4 B C L B DE Algebra ——————————————————————— 3 8 85 10

5 J A 4 n A 2 10 LMN For usewiththelesson“ProveTriangles SimilarbySSSandSAS” Practice m Find thevalue of 12 A , Z Y K 9 EF or

C 5 10 16 n

m RST

1 Not drawntoscal 5,and B similarto 85 X M N M N m 4 thatmakes 12 L 8 5 B

8 4.5 > e

n ABC 6 E . n ABC ? 12 T S

4. S T , 5

n 10 6 9 R DEF 6 L J n R 5 A

A when to 9 n K B AB . 18 Date Z X

5 3, ———————————— BC B 16

5 4, Y

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Name Thesidelengthsof 9. triangles canbesimilar. Sketch thetrianglesusinggivendescription. C. A. 8. 6. Explain Show thatthetrianglesaresimilarandwriteasimilaritystatement. LESSON

Thesidelengthsof 6.4 R Multiple Choice n Q 2 ——————————————————————— 6 ACE P yourreasoning.

} 35 12 2

For usewiththelesson“ProveTriangles SimilarbySSSandSAS” Practice 4 ,

n T 10 DCB In the diagram attheright, Inthediagram 8 . Find thelengthof n n DEF ABC S

continued ae1,2 n 6 In are16,20and26. are8,10and14. D. B.

} 18 30 7 AB }

10. 7.

In G Explain n n H DEF 10 C ABC

B , , whetherthetwo 8 14 DE AB 7 A

5 5 Date D E 15, 5, K 6 EF 3.5 ———————————— BC 4

5 M 8and N 24and Practice Workbook m m E Geometry

5 B

38°. 5 38°. 113 114 Name Pine Tree In Exercises15and16,usethefollowinginformation. 14. 13. 12. 11. In Exercises11–14,usethediagramatright which is11feetfromthebaseoftree. mirror The studentis6feettallandstands3fromthe stands where shecanseethetopoftree,asshown. and ontheground pine tree,astudentplacesmirror to copyandcompletethestatement. 16. 15. Practice Workbook Geometry LESSON Anotherstudentalsowants toseethetopof Whatistheheight 6.4

mirror beplaced? mirror how fromthebaseoftreeshould far istoremain3feetfromthestudent’smirror feet, tree. The otherstudentis5.5feettall.Ifthe m AB m n ——————————————————————— ABC

5 CAB DCE Inordertoestimatetheheight ?

For usewiththelesson“ProveTriangles SimilarbySSSandSAS” Practice ,

1 5 ?

? m ABC h (infeet)ofthepinetree?

5 ? continued h ofatall

D 6 ft A C 16 3ft 12 14 135 Date 8 E B 11 ft

———————————— h

Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Determine thelengthofeachsegment. 9. Use thegiveninformationtodeterminewhether Use thefiguretocompleteproportion. Name

14. 13. 12. 11. 7. 5. 3. 1. LESSON

6.5 E } } } CD } GB } FC } BC } A AG CD GC CF FB FG ——————————————————————— 3

5 5

5 B 3 } FB } }

GD DB For usewiththelesson“UseProportionalityTheorems” Practice ? ? ? A

5 C B 11 9 8 C D

6. 4. 2. 4

E } } } GD CD FC AF

GE AE

} BD }

} AE ? ? ?

E 10. 7 8. F 5 G

5 C A A BD }

6 5 15 i 2

AE }

B B .

B 1.2 3 6 C A 1 Date C F D C A ———————————— D 9 G D D B E E Practice Workbook 7.5 E Geometry 115 116 of equalparts. Use constructiontoolstodividethelinesegment intothegivennumber Find thevalueofvariable. ﬁndthevalueof In Exercises15–18, Name 15. 24. 23. 22. 21. 20. 19. 17. Practice Workbook Geometry LESSON 2 2 3 4 6.5 a m x ——————————————————————— 010 10 8 5 44 For usewiththelesson“UseProportionalityTheorems” Practice 2 45 8 x x

continued LM LM LM 3 5 x . 18. 16. m 6 x 14 6 110 70 2 8 8 x 3 4 x Date a 3.5 ———————————— 9 3 2

25. LESSON

6.5 300 ft 600 ft b. point from point Maps a. ——————————————————————— Park Ave. Park Avenue to51stStreet.IsPark isperpendicular Avenue to perpendicular How many morefeetdidCharliewalk thanyou? 52nd Street? B C A For usewiththelesson“UseProportionalityTheorems” Practice On themapbelow, 51stStreet and52ndStreetareparallel.Charliewalks topoint A topoint C Explain 1200 ft . B andthenfrompoint . continued 500 ft A Wayne St. B topoint C . You walk directly from 52 51 st st St. St. Date ———————————— Practice Workbook Geometry 117 118

an Determine whetherthedilationfromFigureAtoBisa Draw adilationoftheﬁgureusinggivenscalefactor. Name 5. 3. 1. Practice Workbook Geometry LESSON enlargement

6.6 k k x ———————————————————————

5 5 2 } 2 1 B y 2

C 1 For usewiththelesson“PerformSimilarityTransformations” Practice y 33 z 1 2 . Then,ﬁndthevaluesofvariables. y A A B B A 6 6 4 D C x x

2. 6. 4.

k k C

5 5 7

1 } 4 1 A 10

} 2 1 C

14 8 A B 1 1 y y Date B 1 1 D reduction n A ———————————— m B x x or

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. translation Determine whetherthetransformationfromFigureAtoBisa Name 11. 9. 7. LESSON

6.6 2 ——————————————————————— A z x 2 For usewiththelesson“PerformSimilarityTransformations” Practice , 55 y reﬂection y 2 B A y 2 7.5 7.5 B B A 3 , rotation x x continued

, or dilation . 12. 10. 8. B 6 A 2 y 2 2 A y 12 Date A 4 B ———————————— x x n 8 B 3 m Practice Workbook Geometry 119 120 Name c.

14. 13. Practice Workbook Geometry LESSON

6.6 b. reduced asshown intheﬁgure. Posters Overhead Projectors enlargement? the wall hasadiameterof4feet. ofthe What isthescalefactor on thewall. The circledrawn hasaradiusof3inches. The circleon projector. The projectorthendisplays anenlargement ofthecircle a. ———————————————————————

How (a)relatedtothescalefactor inpart arethescalefactors Asecondposterisreduceddirectly fromsize A tosizeC. oftheenlargement? Whatisthescalefactor thereduction? in part (b)? in part ofthereduction? What isthescalefactor . n 17in. 8.5 in. For usewiththelesson“PerformSimilarityTransformations” Practice A posterisenlarged andthen theenlargement is 11 in. ABC Your teacherdraws acircleonanoverhead continued 22 in.

Date 4.25 in. ———————————— 5.5 in. 3 in. 4 ft

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. the lengthofthirdsideandtellwhether itisalegorthehypotenuse. of thetriangleareintegersandtogetherform aPythagoreantriple.Find The givenlengthsaretwosidesofarighttriangle. Allthreesidelengths Tell whetherthesidelengthsformaPythagoreantriple. Find theunknownsidelength.Simplifyanswersthatareradicals. Use Name 13. 10. 3. 2. 1. 7. 6. 5. 4. LESSON

7.1 n 10 a c c b c b 40 and41 ——————————————————————— 2 2 2 2 2 2 7 ABC

5 5 2 5 2 1

b a a c c a 2 2 2 2 2 2 todetermineiftheequationis For usewiththelesson“ApplyPythagoreanTheorem” Practice

2 1 2 5 5 5

b a b a b x c 2 2 2 2 2 2 x 19

14. 11. 8.

b x 12 and35 C A x 8 true 13 12 2 or

c a false x .

15. 12. B 9. Date 63 and65 6 ———————————— x x 6 5 15 Practice Workbook Geometry 121 122 Name Round decimalanswerstothenearesttenth. Find theareaofﬁgure.Rounddecimalanswerstonearesttenth. Find theareaofarighttrianglewithgivenleg 31. 28. 25. 22. 19. 16. Practice Workbook Geometry LESSON

7.1 7 ft * * 80 and89 28 and45 ———————————————————————

5 5 9mi, 8m, For usewiththelesson“ApplyPythagoreanTheorem” Practice h 62 m 26 m h

5 10 ft 16m 10mi

30 m continued

32. 29. 26. 23. 20. 17. 48and55 56and65 4 cm * *

3 5 5 i n. 21in., 9yd, 4 in. h 13 in.

h 5

5 12yd 12 cm * 29in. andhypotenuse

24. 21. 18. 33. 30. 27. Date 65and72 20and29

* * 14 in. 20 ft

5 5 h ———————————— 3.5ft, 13cm, . 16 ft 11 in. h h

5 20 in.

5 9ft 17cm 10 ft

Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Garden usethefollowinginformation. In Exercises36–38, Name 36. 38. 37. 35. 34. LESSON Find theperimeterofgarden. You plantoattachfencingtheposts You aregoingtoplantapostevery 7.1 Find theothertwo distancesbetween cities. between thetwo apart. citiesthatarefurthest back tocity A) is1400miles.It600miles distance (fromcity A tocityBCand ofarighttriangle. vertices The totalflight flies tothreecitieswhosethe locationsform garden? how muchwillitcosttoenclosethe $1.25 andeachfootoffencingcosts$.70, to enclosethegarden.Ifeachpostcosts How many posts doyou need? 15 inchesaroundthegarden’s perimeter. Flight Distance catcher mustthrow asoftballfrom3feetbehindhomeplatetosecondbase. consecutive rightangles.Find basesis65feetandthepathsform distance Softball ——————————————————————— You have agardenthatisin theshapeofarighttrianglewithdimensionsshown. For usewiththelesson“ApplyPythagoreanTheorem” Practice Inslow-pitch softball,thedistanceofpathsbetween eachpairof Explain Asmallcommuterairline . continued

88 in. City C City B 600 mi x Date in. 137 in. ———————————— City A

Practice Workbook Geometry 123 124

Decide whether Graph points 1. If theycan,classifythetriangleas Decide whetherthenumberscanrepresentsidelengthsofatriangle. Name 9. 7. 4. Practice Workbook Geometry LESSON

7.2 A A 15, 36,39 5, 12,13 ——————————————————————— (4, 1), ( 2 2 3, 5), y For usewiththelesson“UseConverseofPythagoreanTheorem” Practice 2 B 2 (7, B A (0, y , 2 2 n B 2), 2 , and ABC 2), C (2, C x x is

(4, 1) C 2 . Connectthepointstoform right 4) , 5. 2. acute

Ï Ï right } } 13 , 10,12 8 , 4,6

, or

, obtuse acute 10. 8.

, or . A A ( ( 2 2 obtuse 8, 2, 2), n 2 ABC 4), 2 B . (6, 4), y B 2 6. 3. ( . 2 2 Date 5, y 14, 48,50 20, 21,28 C 2 2 ( ———————————— x x 2 2), 4, 10) C ( 2 1, 2 7)

the longestsideisintegergiven.Whatvalue(s)of The sidesandclassiﬁcationofatrianglearegivenbelow. Thelengthof if possible.Ifitisnotpossible, In Exercises13and14,copycompletethestatementwith<,>,or Name 19. 17. 11. 15. 14. 13. LESSON

7.2 m m A x x x ——————————————————————— , , , 1 (0, 5), x x x , 6;acute , 8;right y K J 2 1 ?

8,40;right 1 For usewiththelesson“UseConverseofPythagoreanTheorem” Practice B

m (3, 6), m 18. L ? R C (5, 1) m x S

continued 1

m explain T why. 12. 20. 16.

12 x x A x J K , , ( 1 x 2 x , 12;obtuse

2, 1 2, 4), 6 3,15;obtuse x 6 x

makethetriangle? 1 L 2 6 B 3,29;acute (2, 0), y 2 Date 14 R C S (5, 2) ———————————— x 8 2 5

65 , T Practice Workbook Geometry 125 126 Name whether youwillusetwodifferentmethodsfordetermining In Exercises23–25, The slopeoftheroofis Roof In Exercises21and22,usethediagramfollowinginformation. 22. 21. 25. 24. 23. Practice Workbook Geometry LESSON Arow ofshinglesis5incheshigh.How many rows Whatisthelengthfromgutter to peakoftheroof? 7.2 Theroofshown attherightisshown inthediagram fromthefrontofhouse. n of thePythagorean whetherTheorem todetermine Method 2 Method 1 Explain whether agiven triangleisright,acute,or obtuse? Compare of shinglesareneededforonesidetheroof? What dotheslopestellyou about a righttriangle?How doyou know? ——————————————————————— ABC n ABC isarighttriangle. For usewiththelesson“UseConverseofPythagoreanTheorem” Practice . Whichmethodwould you usetodetermine UsetheDistanceFormula andtheConverse Find theslopeof isarighttriangle. } 12 5

. The heightoftheroofis15feet. continued AC AC } andtheslopeof

ACB ? Is n ABC BC }

5 in. B ( 2 3, 7) Shingle Date 1 C y (0, 3) 1 ———————————— A

(4, 6) x

altitude tothehypotenuse.Rounddecimalanswers tothenearesttenth. Tell whether thetriangleisarighttriangle.Ifso,ﬁndlengthof Find thevalue(s)ofvariable(s). Complete andsolvetheproportion. Name 10. 1. 7. 4. LESSON

7.3 12

} 12 x ———————————————————————

5 818

} 8 ?

For usewiththelesson“UseSimilarRightTriangles” Practice w x 12 14 1 2

9 12 85 a 8

11. 8. 5. 2.

} 15 x 15

y 5 z 68

} ? x x

14 x 6 16 20 19 x 15 19

12. 6. 3. 9. Date

10 } 9 x

9 5 b ————————————

} ? x 30 c

x 11 a 24 32 6 Practice Workbook 34 24 b Geometry 18 127 128 3. 2. 1. Use theGeometricMeanTheoremstoﬁnd Name 7. 6. 5. 4. Statements 16. 13.

? Practice Workbook Geometry n n n VW } LESSON

7.3 XYZ XYZ YUZ Z VWZ A PROVE: GIVEN: Complete theproof.

——————————————————————— > i

XY } 30

isaright

, >

n For usewiththelesson“UseSimilarRightTriangles” Practice YUZ VWZ

D B

XYZ

n n } VW XYZ YUZ n

i withaltitude

XY } isarighttrianglewith 40

, ,

n YU } VWZ isanaltitudeof C

continued YU } 14. . 10 A B m n XYZ XYZ 6 AC . C

5 and 90

2. 1. Reasons 7. 6. 5. 4. 3. 8 . ? ? ? AA Similarity Postulate ? ? ?

BD D

. 15. Date

C ———————————— X Y 35 5 U W V D B Z A

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. In Exercises17–19,usethediagram. Name 20. 19. 18. 17. LESSON Whichsegment’s lengthisthegeometricmeanof Writesimilaritystatementsforthethreetriangles. Sketch thethreesimilartrianglesindiagram. 7.3 Label thevertices. LM Kite Design long shoulditbe? kite. You know that BC You want touseastraightcrossbar ———————————————————————

and 5 72centimeters,and For usewiththelesson“UseSimilarRightTriangles” Practice JM ? You aredesigningadiamond-shaped AB

5 38.4centimeters, continued AC

5 81.6centimeters. BD } . About how

D J A Date B ———————————— M K C

Practice Workbook L

Geometry 129 130 radical form. Find thevalueofeachvariable.Writeyouranswersinsimplest Find thevalueof Name 10. 4. 1. 7. Practice Workbook Geometry LESSON

7.4 5 6 ——————————————————————— 212 12 45 3 30 8 60 16 8 For usewiththelesson“SpecialRightTriangles” Practice 8 x x x 45 x y 8 30 x

8 y . Writeyouranswerinsimplestradicalform.

11. 8. 5. 2.

11 9 60 45 2 30 8 8 8 y 8 x x 8 x y 60 45 x

8 8 x

12. 6. 3. 9. Date

x 13 45 ———————————— 30 30 5 8 3 x 8 y 8 2 18 y 9 45 8 2 60 8 x x

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. radical form. Find thevalueofeachvariable.Writeyouranswersinsimplest Complete thetable. Name 18. 15. 13. y x LESSON

7.4 ——————————————————————— 5 60 a 45 b 8 xx 10 8 4 For usewiththelesson“SpecialRightTriangles” Practice r Ï } 2

y 6

Ï } 2 s

45 8 6 9

continued 24 19. 16.

p 2 n

8 24 d 30 c 14.

n 8 c b a 30

8 911 b c 20. 17. 9 Date

h 60 5 x 8 ———————————— a

Ï 8 g } 3 y 105

16 f 30 x Practice Workbook 8 12 16 Geometry 131 132 Name

maximumheighttobe56centimetersasshown. toinclineatanangleof30 rampsurface apyramid-shaped skateboardramp. You want each 45 The sidelengthsofatrianglearegiven.Determinewhetheritis

unitforeach1horizontalunit. atarateof1vertical bothsides,which meansthatitslopesupward areaoftheroof. The roofhasa1-1pitchon houseshown, andyou want toknow thetotal 25. 24. 21. Practice Workbook Geometry 8 LESSON 5,10,5 -45 7.4 b. b. Rooﬁng Skateboard Ramp a. a. ——————————————————————— Suppose you want tobuildasecondpyramid ramp Usetherelationshipsshown to inthediagram Find thetotalareaofrooftonearestsquarefoot. Find thevalues of 8 -90 for thisramp. the lengths simply changingthe30 of 56inches. You shown canusethediagram by with a45 centimeter. thelengths determine 8 For usewiththelesson“SpecialRightTriangles” Practice Ï triangle, You arereplacingtheroofon } 3

8 angleofinclineandamaximumheight a , b a ,

c o r sn odt ul You areusingwood tobuild , and 30 x and 8 -60 a continued d 8 , angleto45 tothenearestcentimeter y b inthediagram. 8 , 22. -90 c , and 7,7 8 triangle, d tothenearest 8 . Determine . Determine 8 and the Ï } 3

or neither.

45 23. 8 d Date 6,6 xy c ———————————— 24 ft Ï } 2

b 45 8 30 8 a 35 ft

5 6

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Compare using the45 Find thevalueof Find thevalueof four decimalplaces. Find tan Name 10. 7. 4. 1. LESSON

7.5 B 25 ——————————————————————— 50 45 x 62 A 8 8 the results. 8 x andtan 53 For usewiththelesson“ApplyTangent Ratio” Practice 10 45 8 -45 x 8 13 -90 x x 5 5. usingthedeﬁnitionoftangent.Thenﬁnd valueof tothenearesttenth. B C 28 A 2 8 . Writeeachanswerasadecimalroundedto Triangle Theoremorthe30 11. 2. 8. 4 9 33 C A 3 43 8 x 56 65 x x 8 30 24 -60 29 B 8 8 3. 9. 8 -90 12. 8 6. Triangle Theorem. Date B 36 72 ———————————— 41 25 9 16 8 8 3 C 15 x x Practice Workbook

12 60 x 8 x Geometry A 133 134 Name Triangle Theoremorthe30 Find theperimeteroftriangle.Roundto thenearesttenth. Find theareaoftriangle.Roundyouranswertonearesttenth. Use atangentratiotoﬁndthevalueof For acute 22. 19. 16. 13. Practice Workbook Geometry LESSON

7.5 x m ——————————————————————— 40 A 8 49 in.

11 m 17 5 For usewiththelesson“ApplyTangent Ratio” Practice 30 A 36 ofarighttriangle,ﬁndtan 8 14. 8 20. 64 23. 8 x 17. continued 8 -60 8 -90

x m 8 Triangle Theorem. 36 A

5 x 24 ft . Roundtothenearesttenth. 45 A byusingthe45 34 ft 8 15. 32 8 43 x 8 71 21. 8 18. 24. 8 -45 Date

8 40 in. m -90 x ———————————— 44 A 8

56 8

5 8 60 8 53 23 62 ft 8 x

7.5 b. the given ﬂights aregiven below. Find therocket’s height Skyscraper elevation you move 100feetfromthelaunchpointandrecordangleof Drive-in Movie foot, how areyou far fromyour friend? top oftheskyscraper is 71 elevation fromyour friend’s positiontothe top oftheskyscraper is 42 angle ofelevation fromyour positiontothe is between theskyscraper andyourself. The skyscraper thatis780feet tall. Your friend screen is58 and theangleofelevation tothetopof horizontal linewiththebottomofscreen screen atadrive-in movie. Your eye isona c. a. ———————————————————————

u u u

5 5 5 For usewiththelesson“ApplyTangent Ratio” Practice 83 81 77 u u 8 8 8 totherocket atitshighestpoint. The values of ineachﬂight. 8 You areablock away from a . How tallisthescreen? You are50feet from the To calculatetheheight continued 8 8 . To thenearest . The angleof h reachedby amodelrocket,

to thenearestfootfor

y ou u

for three 58 42 50 ft 8 8 your friend Date

———————————— 71

8 0 ft 100 780 ft h Practice Workbook

Geometry 135 136 7. Round tofourdecimalplaces,ifnecessary. Find cos Round tofourdecimalplaces,ifnecessary. Find sin Name 10. 1. 4. Practice Workbook Geometry LESSON

7.6 14 S 20 A C ——————————————————————— C A TS R 40 R A andsin andcos For usewiththelesson“ApplySineandCosineRatios” Practice 15 52 48 58 25 T 48 50 42 2. S B . Writeeachanswerasafractionanddecimal. . Writeeachanswerasafractionanddecimal. B 20 R 5. 8. B 11.

12 S 28 A C A S T 48 45 53 26 C 73 35 24 37 55 R

6. B 10 T R

12. B 3. 9. Date

B 18 16 R S B C T ———————————— 65 125 24 30 C 30 97 34 117 A 72

S 44 R T A

Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. decimal places,ifnecessary. answer asafractioninsimplestformanddecimal.Roundtofour Find theunknownsidelength.Thenfindsin Use the45 to thenearesttenth. Use acosineorsineratiotofindthevalueofeachvariable.Rounddecimals Name to findthesineandcosineofangle. 22. 19. 13. 16. 24. LESSON a 30

7.6 B a A ——————————————————————— 33 57 8 t 8 angle C For usewiththelesson“ApplySineandCosineRatios” Practice 8 6 -45 14 32 b 8 -90 56 C B 2 51 u 8 Triangle Theoremorthe30 7 25. 14. 17. A

23. continued 20. x a 45 47 41 c 8 angle 8 8 y d 12 A andcos 8

-60 17 A 36 18. 3 B C

8 -90 7 15. 8 Triangle Theorem A C 12 . Writeeach 85 21. Date a 60 A B 44 ———————————— 39

36 8 angle 8 s r g Practice Workbook h 21 Geometry 137 138 Name

28. 27. 26. Practice Workbook Geometry LESSON

7.6 b. the ground andtheladder.the ground you shouldalways useanangleofabout75.5 its minimumlengthtomaximumlength.For safety, an extension ladderrangesinone-footincrementsfrom to paintachimney thatis33feettall. The lengthof Ski Lift height 4640 feet. To thenearest foot,what isthevertical of elevation of28 Extension Ladders Airplane Landing answer tothenearestfoot. when you are500feetabove Roundyour theground? d a3 forms airplane. You areonastraightlineapproachpaththat c. a. ——————————————————————— along thisapproachpathtoyour touchdown point You placethebaseofladder3feetfrom Your smallestextension ladderhasamaximum chimney. How many feetlongshouldtheladder be? wall?reach onavertical length of17feet.How highdoesthisladdersafely the ladderbe? that reaches30feethigh.How many feetlongshould To reachthetopofchimney, you needaladder h For usewiththelesson“ApplySineandCosineRatios” Practice Achairliftonaskislopehasanangle covered by thechairlift? 8 anglewiththerunway. What isthedistance 8 andcovers atotaldistanceof You arepreparingtolandan You areusingextension ladders continued 8 between

Approach path 75.5 4640 ft 28 8 8 Date

3 ———————————— d Not drawntoscale h

500 ft

Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Solve therighttriangle.Rounddecimalanswerstonearesttenth. to thenearesttenth. Use thediagramtofindindicatedmeasurement.Roundyouranswer Name 10. 2. 1. 7. 4. 3. LESSON

7.7 V A m m MN P ——————————————————————— N M 26 For usewiththelesson“SolveRightTriangles” Practice 8 14 4.5 22 37 51 N 8 B D M R

15 11. 8. 5. 11 R W P M P 7 T V 33 18 20 12 8 24 N A

12. 6. 9. Date U U J

7 ———————————— 31.6 K 23 8 28 M Practice Workbook L 19 S 7 Geometry T E 139 140 Name

Let 17. 13. 22. 21. Practice Workbook Geometry A LESSON tan sin

tothenearesttenthofadegree. 7.7 suspension bridge. SuspensionBridge Office Buildings apart arethebuildings? apart of a200footofficebuildingis55 the topofa320footofficebuildingto ——————————————————————— A beanacuteangleinarighttriangle.Approximatethemeasureof A A 32

5 5 8 For usewiththelesson“SolveRightTriangles” Practice 0.36 0.42 52 ft 32 Theangleofdepressionfrom 8 Use the diagram toﬁndthedistanceacross Usethediagram 18. 14. cos tan 32 continued 8 A A

5 5 52 ft 8 0.8 . How far 0.11 32 8 32 19. 15. 8

sin sin 320 ft 52 ft A A 32

5 5 8 0.94 0.27 Date x 55 8 ———————————— 20. 16. cos cos 200 ft A A

5 5

0.77 0.35

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. can seetwo people. Balloon Hot Air usethefollowinginformation. In Exercises25–27, Ramps In Exercises23and24,usethefollowinginformation. Name must belessthanorequalto4.78 specify thattherampangleusedforawheelchair ramp 600 ft 27. 26. 25. 24. 23. LESSON You want riseof6inches. tobuildarampwithvertical You want tominimizethe Thelengthofonerampis16feet. rise is14inches.Estimatetheramp’sThe vertical How arethetwo apart far people? Iftheangleofdepressionfromyour lineofsighttothepersonat Iftheangleofdepressionfromyour lineofsighttothepersonat 7.7 dimensions ofyour ramp. horizontal distancetaken upby theramp.Draw asketch showing theapproximate Accessibility Standards? Federalhorizontal distanceanditsrampangle.DoesthismeettheUniform the person from the point on the ground belowthe personfrompointonground the hotairballoon? the person from the point on the ground belowthe personfrompointonground the hotairballoon? ——————————————————————— Not drawntoscale The Uniform FederalThe Uniform Accessibility Standards For usewiththelesson“SolveRightTriangles” Practice You areinahotairballoonthatis600feetabove where theground you B continued 8 . C

length oframp horizontal distance C B ramp angle is30 is20 Date 8 8 , how is far ———————————— , how is far Practice Workbook rise vertical Geometry

141 Name ——————————————————————— Date ————————————

LESSON Practice 8.1 For use with the lesson “Find Angle Measures in Polygons”

Find the sum of the measures of the interior angles of the indicated convex polygon. 1. Hexagon 2. Dodecagon 3. 11-gon

4. 15-gon 5. 20-gon 6. 40-gon

The sum of the measures of the interior angles of a convex polygon is given. Classify the polygon by the number of sides. 7. 1808 8. 5408 9. 9008

10. 18008 11. 25208 12. 39608

13. 50408 14. 59408 15. 86408

Find the value of x.

16. 142 17. 18. 158 105 64 146 16x 140

86 110

Geometry 142 Practice Workbook Name ——————————————————————— Date ————————————

LESSON Practice continued 8.1 For use with the lesson “Find Angle Measures in Polygons”

19. 20. 21. 75 93 60 60 8x x 90 2x 4x 100 2x 20 6x x 6x

22. What is the measure of each exterior angle of a regular nonagon?

23. The measures of the exterior angles of a convex quadrilateral are 908, 10x8, 5x8, and 458. What is the measure of the largest exterior angle?

24. The measures of the interior angles of a convex octagon are 45x8, 40x8, 1558, 1208, 1558, 38x8, 1588, and 41x8. What is the measure of the smallest interior angle?

Find the measures of an interior angle and an exterior angle of the indicated polygon. 25. Regular triangle 26. Regular octagon 27. Regular 16-gon

Geometry Practice Workbook 143 Name ——————————————————————— Date ————————————

LESSON Practice continued 8.1 For use with the lesson “Find Angle Measures in Polygons”

In Exercises 31–34, ﬁnd the value of n for each regular n-gon described. 31. Each interior angle of the regular n-gon has a measure of 1408.

32. Each interior angle of the regular n-gon has a measure of 175.28.

33. Each exterior angle of the regular n-gon has a measure of 458.

34. Each exterior angle of the regular n-gon has a measure of 38.

35. Storage Shed The side view of a storage shed is shown below. Find the value of x. Then determine the measure of each angle.

A 2x E B 2x 2x

D C

36. Tents The front view of a camping tent is shown below. Find the value of x. Then determine the measure of each angle.

P O 140 Q 150 150 N R (2x 1 20) (2x 1 20)

M x x S

37. Proof Because all the interior angle measures of a regular n-gon are congruent, you can find the measure of each individual interior angle. The measure of each (n 2 s interior angle of a regular n-gon is } . Write a paragraph proof to prove n this statement. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifflin Harcourt Publishing Company.

Geometry 144 Practice Workbook Name ——————————————————————— Date ————————————

LESSON Practice 8.2 For use with the lesson “Use Properties of Parallelograms”

Find the measure of the indicated angle in the parallelogram. 1. Find mB. 2. Find mG. 3. Find mM.

B C F G K L 132 96

64 A D E H J M

Find the value of each variable in the parallelogram.

4. b 5. x 1 2 6. 16 (y 60) y 2 5 a 9 12 56 4 3x 4 11

7. (f 30) 8. 9. 9 3m 3j 6k 25 8g 3 1 2 k 1 10 2 72 m 8 2n 1 5j 9

10. In ~WXYZ, mW is 50 degrees more 11. In ~EFGH, mG is 25 degrees less than mX. Sketch ~WXYZ. Find the than mH. Sketch ~EFGH. Find the measure of each interior angle. Then label measure of each interior angle. Then label each angle with its measure. each angle with its measure. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company.

Geometry Practice Workbook 145 Name ——————————————————————— Date ————————————

LESSON Practice continued 8.2 For use with the lesson “Use Properties of Parallelograms”

Find the indicated measure in ~ABCD.

12. mAEB 13. mBAE A B 238 808 E 8 14. mAED 15. mECB 117 D C

16. mBAD 17. mDCE

18. mADC 19. mDCB

} Use the diagram of ~MNOP. Points Q, R, S, and T are midpoints of MX , } } } NX , OX , and PX . Find the indicated measure.

20. PN M N R 37 3 X 5 21. MQ 132 S 125 T P O

22. XO

23. mNMQ

24. mNXO

25. mMNP

26. mNPO

Geometry 146 Practice Workbook Name ——————————————————————— Date ————————————

LESSON Practice continued 8.2 For use with the lesson “Use Properties of Parallelograms”

28. Movie Equipment The scissor lift shown at the right is sometimes used by camera crews to film movie scenes. The lift can be raised or lowered so that the camera can get a variety of views of one scene. In the figure, points E, F, G, and H are the vertices of a parallelogram. a. If mE 5 45°, find mF. F

E G H

b. What happens to E and F when the lift is raised? Explain.

29. In parallelogram RSTU, the ratio of RS to ST is 5 : 3. Find RS if the perimeter of ~RSTU is 64.

30. Parallelogram MNOP and parallelogram N O PQRO share a common side, as shown. Using a two-column proof, prove that segment MN is congruent to segment QR.

Geometry Practice Workbook 147 Name ——————————————————————— Date ————————————

LESSON Practice 8.3 For use with the lesson “Show that a Quadrilateral is a Parallelogram”

What theorem can you use to show that the quadrilateral is a parallelogram?

1. 75 105 2. 73

98 98

105 73

3. 4. 3.6 10 5 5 3.6 10

For what value of x is the quadrilateral a parallelogram?

5. 2x 2 1 6.

x 1 5 3x 2 11 x 1 5

7. 8. 8x 101 x

3x 1 5 101

9. 10. (5x 7)

(x 1)

Geometry 148 Practice Workbook Name ——————————————————————— Date ————————————

LESSON Practice continued 8.3 For use with the lesson “Show that a Quadrilateral is a Parallelogram”

The vertices of quadrilateral ABCD are given. Draw ABCD in a coordinate plane and show that it is a parallelogram. 11. A(22, 23), B(0, 4), C(6, 4), D(4, 23) 12. A(23, 24), B(21, 2), C(7, 0), D(5, 26)

y y

1 2

1 x 2 x

Describe how to prove that ABCD is a parallelogram.

13. B 14. A B C

A D C D

15. Three vertices of ~ABCD are A(21, 4), B(4, 4), and C(11, 23). Find the coordinates of point D. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company.

Geometry Practice Workbook 149 Name ——————————————————————— Date ————————————

LESSON Practice continued 8.3 For use with the lesson “Show that a Quadrilateral is a Parallelogram”

16. History The diagram shows a battering ram H which was used in ancient times to break through G walls. A log is suspended on ropes of equal } } J length (GF and HJ ). The log swings, causing F }quadrilateral} FGHJ} to shift. In the diagram, GH > FJ and GH is parallel to the ground. a. Identify FGHJ. Explain.

b. Explain why the log is always parallel to the ground.

17. Proof Use the diagram at the right. B C

GIVEN: nABC > nCDA

PROVE: ABCD is a parallelogram.

Geometry 150 Practice Workbook Name ——————————————————————— Date ————————————

LESSON Practice 8.4 For use with the lesson “Properties of Rhombuses, Rectangles, and Squares”

For any rhombus ABCD, decide whether the statement is always or sometimes true. Draw a diagram and explain your reasoning. } } 1. ABC > CDA 2. CA > DB

For any rectangle FGHJ, decide whether the statement is always or sometimes true. Draw a diagram and explain your reasoning. } } 3. F > H 4. GH > HJ

Classify the quadrilateral. Explain your reasoning. 5. 6. 91

Name each quadrilateral—parallelogram, rectangle, rhombus, and square—for which the statement is true. 7. It is equilateral. 8. The diagonals are congruent. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company.

9. It can contain obtuse angles. 10. It contains no acute angles.

Geometry Practice Workbook 151 Name ——————————————————————— Date ————————————

LESSON Practice continued 8.4 For use with the lesson “Properties of Rhombuses, Rectangles, and Squares”

Classify the special quadrilateral. Explain your reasoning. Then ﬁnd the values of x and y. 2y 1 4 11. A B 12. T 127

5y 1 1 3x S (2x 1) U

6y 5 3y 7 D 5x 2 4 C V

The diagonals of rhombus PQRS intersect at T. Given that mRPS 5 308 and RT 5 6, ﬁnd the R indicated measure. 6

13. mQPR 14. mQTP T

P 30 S

15. RP 16. QT

The diagonals of rectangle WXYZ intersect at P. W X Given that mYXZ 5 508 and XZ 5 12, ﬁnd the indicated measure. 50 17. mWXZ 18. mWPX P Z Y

19. PY 20. WX

The diagonals of square DEFG intersect at H. D E Given that EH 5 5, ﬁnd the indicated measure. 5 21. mGHF 22. mDGH H

G F

Geometry 152 Practice Workbook Name ——————————————————————— Date ————————————

LESSON Practice continued 8.4 For use with the lesson “Properties of Rhombuses, Rectangles, and Squares”

25. Windows In preparation for a storm, a window is protected by nailing boards along its diagonals. The lengths of the boards are the same. Can you conclude that the window is square? Explain.

26. Clothing The side view of a wooden clothes dryer 9 2 is shown at the right. Measurements shown are in inches. a. The uppermost quadrilateral is a square. Classify the quadrilateral below the square. h Explain your reasoning.

24 b. Find the height h of the clothes dryer.

27. Proof The diagonals of rhombus ABCD form several triangles. Using a two-column proof, prove that nBFA > nDFC.

GIVEN: ABCD is a rhombus. B C

PROVE: nBFA > nDFC

Geometry Practice Workbook 153 Name ——————————————————————— Date ————————————

LESSON Practice 8.5 For use with the lesson “Use Properties of Trapezoids and Kites”

Points A, B, C, and D are the vertices of a quadrilateral. Determine whether ABCD is a trapezoid. 1. A(22, 3), B(3, 3), C(21, 22), D(2, 22)

2. A(23, 2), B(3, 0), C(4, 3), D(22, 5)

3. A(25, 23), B(21, 21), C(21, 3), D(23, 2)

Find mF, mG, and mH.

4. F 5. F J 68 J 110

H G H G

Find the length of the midsegment of the trapezoid.

6. 21 7. M

64 82 M N

Geometry 154 Practice Workbook Name ——————————————————————— Date ————————————

LESSON Practice continued 8.5 For use with the lesson “Use Properties of Trapezoids and Kites”

JKLM is a kite. Find mK.

8. J 9. M

J 60 50 L

K M 88 K 120 L

Use Theorem 8.18 and the Pythagorean Theorem to ﬁnd the side lengths of the kite. Write the lengths in simplest radical form.

10. S 11. S

5 V T 8 5 5 99 V T 12 7

U U

Find the value of x.

12. 10 13. M

2x 1 4332 4x M N

N 44

14. 2x 15. 808

17.1 N M 2x8 1118

Geometry Practice Workbook 155 Name ——————————————————————— Date ————————————

LESSON Practice continued 8.5 For use with the lesson “Use Properties of Trapezoids and Kites”

16. Maps Use the map shown at the right. y The lines represent a sidewalk connecting Pool Tennis court Miniature the locations on the map. golf course a. Is the sidewalk in the shape of a kite? Explain. Arcade Basketball 1 court Restaurant b. A sidewalk is built that connects the arcade, 1 x tennis court, miniature golf course, and restaurant. What is the shape of the sidewalk?

c. What is the length of the midsegment of the sidewalk in part (b)?

17. Kite You cut out a piece of fabric in the shape of a kite so that the congruent angles of the kite are 1008. Of the remaining two angles, one is 4 times larger than the other. What is the measure of the largest angle in the kite?

} 18. Proof MN is the midsegment of isosceles trapezoid FGHJ. Write F J a paragraph proof to show that FMNJ is an isosceles trapezoid. M N

Geometry 156 Practice Workbook Name ——————————————————————— Date ————————————

LESSON Practice 8.6 For use with the lesson “Identify Special Quadrilaterals”

Complete the chart. Put an X in the box if the shape always has the given property.

Property ~ Rectangle Rhombus Square Kite Trapezoid

1. Both pairs of opposite sides are congruent.

2. Both pairs of opposite angles are congruent.

3. Exactly one pair of opposite sides are congruent.

4. Exactly one pair of opposite sides are parallel.

5. Exactly one pair of opposite angles are congruent.

6. Consecutive angles are supplementary.

Give the most speciﬁc name for the quadrilateral. Explain.

7. 8. 10

10 10

Geometry Practice Workbook 157 Name ——————————————————————— Date ————————————

LESSON Practice continued 8.6 For use with the lesson “Identify Special Quadrilaterals”

9. 10.

Tell whether enough information is given in the diagram to classify the quadrilateral by the indicated name. 11. Rectangle 12. Isosceles trapezoid

658 1158

1158 658

13. Rhombus 14. Kite

Points A, B, C, and D are the vertices of a quadrilateral. Give the most specific name for ABCD. Justify your answer. 15. A(2, 2), B(4, 6), C(6, 5), D(4, 1) 16. A(25, 1), B(0, 26), C(5, 1), D(0, 3) Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifflin Harcourt Publishing Company.

Geometry 158 Practice Workbook Name ——————————————————————— Date ————————————

LESSON Practice continued 8.6 For use with the lesson “Identify Special Quadrilaterals”

In Exercises 17 and 18, which two segments or angles must be congruent so that you can prove that FGHJ is the indicated quadrilateral? There may be more than one right answer. 17. Kite 18. Isosceles trapezoid

G F

J FH H

J G

19. Picture Frame What type of special quadrilateral is the stand of the picture frame at the right?

20. Painting A painter uses a quadrilateral shaped piece of canvas. The artist begins by painting lines that represent the diagonals of the canvas. If the lengths of the painted lines are congruent, what types of quadrilaterals could represent the shape of the canvas? If the painted lines are also perpendicular, what type of quadrilateral represents the shape of the canvas? Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company.

Geometry Practice Workbook 159 Name ——————————————————————— Date ————————————

LESSON Practice 9.1 For use with the lesson “Translate Figures and Use Vectors”

Use the translation (x, y) m (x 1 6, y 2 3). 1. What is the image of A(3, 2)? 2. What is the image of B(24, 1)?

3. What is the preimage of C9(2, 27)? 4. What is the preimage of D9(23, 22)?

The vertices of n ABC are A(21, 1), B(4, 21), and C(2, 4). Graph the image of the triangle using prime notation. 5. (x, y) m (x 2 3, y 1 5) 6. (x, y) m (x 2 4, y 2 2)

y y

1 x 2

2 x

n A9B9C9 is the image of n ABC after a translation. Write a rule for the translation. Then verify that the translation is an isometry.

7. B9 y 8. y B

A9 B A C C9 A B9 1

Geometry 160 Practice Workbook Name ——————————————————————— Date ————————————

LESSON Practice continued 9.1 For use with the lesson “Translate Figures and Use Vectors”

Name the vector and write its component form.

9. 10. 11. D M Y

J X R

Use the point P(5, 22). Find the component form of the vector that describes the translation to P9. 12. P9(2, 0) 13. P9(8, 23) 14. P9(0, 4) 15. P9(25, 24)

The vertices of n ABC are A(1, 2), B(2, 6), and C(3, 1). Translate n ABC using the given vector. Graph n ABC and its image. 16. 8, 2¯ 17. 27, 23¯

y y

Geometry Practice Workbook 161 Name ——————————————————————— Date ————————————

LESSON Practice continued 9.1 For use with the lesson “Translate Figures and Use Vectors”

Find the value of each variable in the translation.

18. y 19. y 3c 1 2 1008 12 a8 2b 5d8 a8 20 13 808 8 c b 2 5 318 x x

20. Navigation A hot air balloon is ﬂying from y point A to point D. After the balloon travels D(14, 12) 6 miles east and 3 miles north, the wind C(8, 8) direction changes at point B. The balloon N travels to point C as shown in the diagram. B(6, 3) A(0, 0) x

a. Write the component form for # AB##Y and #BC##Y .

b. The wind direction changes and the balloon travels from point C to point D. Write the component form for CD# ##Y .

c. What is the total distance the balloon travels?

d. Suppose the balloon went straight from A to D. Write the component form of the

Geometry 162 Practice Workbook Name ——————————————————————— Date ————————————

LESSON Practice 9.2 For use with the lesson “Use Properties of Matrices”

Use the diagram to write a matrix y B C to represent the polygon. A D 1. n CDE 2

1 x

2. n ABF E F

3. Quadrilateral BCEF

4. Hexagon ABCDEF

Add or subtract.

28 4 4 6 5. f6 3g 1 f1 9g 6. 1 F 4 25G F 6 21G

5 22 1 3 7. F 2 4G 1 F 6 24G 8. f20.3 1.8g 2 f0.6 2.7g 27 2 6 21

1.4 1.3 21.4 23 21 29 5 9 9. 2 10. 25 26.5 2 3.9 4 F 0 2G F 26 27G F G F G 2 4 1.3 3.9 Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company.

Geometry Practice Workbook 163 Name ——————————————————————— Date ————————————

LESSON Practice continued 9.2 For use with the lesson “Use Properties of Matrices”

Find the image matrix that represents the translation of the polygon. Then graph the polygon and its image. A B C M N O P 21 5 3 3 7 5 1 11. F G; 5 units right and 12. F G; 6 units left and 2 2 6 3 units down 1 2 6 5 2 units up

y y

2 2

2 x 2 x

Multiply. 26 3 22 3 21 4 13. f4 23g 14. f20.8 4g 15. F 2G F 21.6G F 5 24GF 7 5G

25 0 0.9 5 3 0 2 5 5 16. 17. f23 2 6g 0 18. 24 F 24 2GF 24 23G F G F 1 0 3GF G 23 2

Use the described translation and the graph of the image to ﬁnd the matrix that represents the preimage. 19. 3 units right and 4 units up 20. 2 units left and 3 units down

y B9 y A9 B9

A9 C9

1 1 1 x 1 x D9

Geometry 164 Practice Workbook Name ——————————————————————— Date ————————————

LESSON Practice continued 9.2 For use with the lesson “Use Properties of Matrices”

21. Matrix Equation Use the description of a translation of a triangle to ﬁnd the value of each variable. What are the coordinates of the vertices of the image triangle? 28 x 28 22 b c r 24 23 1 5 F 4 4 y G F d 25 2G F 7 s 6G

22. Office Supplies Two offices submit supply Office 1 Office 2 lists. A weekly planner costs $8, a chairmat 15 weekly planners 25 weekly planners costs $90, and a desk tray costs $5. Use matrix multiplication to find the total cost of supplies 5 chair mats 6 chair mats for each office. 20 desk trays 30 desk trays

23. School Play The school play was performed on three evenings. The attendance on each evening is shown in the table. Adult tickets sold for $5 and student tickets sold for $3.50.

Night Adults Students First 340 250 Second 425 360 Third 440 390

a. Use matrix addition to ﬁnd the total number of people that attended each night of the school play.

Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifflin Harcourt Publishing Company. b. Use matrix multiplication to find how much money was collected from all tickets each night.

Geometry Practice Workbook 165 Name ——————————————————————— Date ————————————

LESSON Practice 9.3 For use with the lesson “Perform Reﬂections”

Graph the reﬂection of the polygon in the given line. 1. x-axis 2. y-axis 3. x 5 21

y B y y A A C

1 1 1 C 1 x AD1 x B 1 x

B C

4. y 5 1 5. y 5 2x 6. y 5 x

y y y

AD AD

1 1 1 C 1 x C 3 x 1 x B C B A

Geometry 166 Practice Workbook Name ——————————————————————— Date ————————————

LESSON Practice continued 9.3 For use with the lesson “Perform Reﬂections”

Use matrix multiplication to find the image. Graph the polygon and its image. A B C A B C D 23 1 6 2 5 7 1 7. Reflect in the x-axis. 8. Reflect in the y-axis. F 4 7 2G F 6 4 25 23G

y y

2 2

2 x 2 x

Write a matrix for the polygon. Then ﬁnd the image matrix that represents the polygon after a reﬂection in the given line. 9. x-axis 10. y-axis 11. x-axis

y B A y y D B C C 1 1 1

1 x B 1 x 2 x

Geometry Practice Workbook 167 Name ——————————————————————— Date ————————————

LESSON Practice continued 9.3 For use with the lesson “Perform Reﬂections”

Find point C on the x-axis so AC 1 BC is a minimum. 12. A(2, 22), B(11, 24) 13. A(21, 4), B(6, 3) 14. A(23, 2), B(26, 24)

The vertices of n ABC are A(22, 1), B(3, 4), and C(3, 1). Reflect n ABC in the first line. Then reflect n A9B9C9 in the second line. Graph n A9B9C9 and n A0B0C 0. 15. In y 5 1, then in y 5 22 16. In x 5 4, then in y 5 21 17. In y 5 x, then in x 5 22

y y y

1 2 2 1 x 2 x 2 x

18. Laying Cable Underground electrical cable is being laid for two new homes. Where along the road (line m) should the transformer box be B placed so that there is a minimum distance from A the box to each of the homes? m Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company.

Geometry 168 Practice Workbook Name ——————————————————————— Date ————————————

LESSON Practice 9.4 For use with the lesson “Perform Rotations”

Match the diagram with the angle of rotation. 1. 2. 3. 8 x8 x x8

A. 1108 B. 1708 C. 508

Trace the polygon and point P on paper. Then draw a rotation of the polygon the given number of degrees about P. 4. 458 5. 1208 6. 1358 B A B AB P A C C C P P D

Rotate the ﬁgure the given number of degrees about the origin. List the coordinates of the vertices of the image. 7. 908 8. 1808 9. 2708

B y C y y

2 C B C

AD B D A 1 x D 1 1

Geometry Practice Workbook 169 Name ——————————————————————— Date ————————————

LESSON Practice continued 9.4 For use with the lesson “Perform Rotations”

Find the value of each variable in the rotation.

10. 11. y 12. 11 24 x 2 4 2s 2 3 y x 1308 1008 1 6 2x 3 8 270 4s x

Find the image matrix that represents the rotation of the polygon about the origin. Then graph the polygon and its image. A B C A B C 1 4 3 0 4 2 13. ; 908 14. ; 1808 F 2 2 4G F2 1 0 3G

y y

1 1

Geometry 170 Practice Workbook Name ——————————————————————— Date ————————————

LESSON Practice continued 9.4 For use with the lesson “Perform Rotations”

A B C D A B C D 1 2 4 5 23 22 2 1 15. ; 908 16. ; 2708 F2 1 3 3 21 G F 24 21 21 24 G

y y

1 1 1 x 1 x

} } } The endpoints of CD are C(2, 1) and D(4, 5). Graph C 9D9 and C 0D0 after the given rotations. 17. Rotation: 908 about the origin 18. Rotation: 1808 about the origin Rotation: 2708 about (2, 0) Rotation: 908 about (0, 23)

y y 2

2 x

Geometry Practice Workbook 171 Name ——————————————————————— Date ————————————

LESSON Practice 9.5 For use with the lesson “Apply Compositions of Transformations” } } The endpoints of CD are C(1, 2) and D(5, 4). Graph the image of CD after the glide reflection. 1. Translation: (x, y) m (x 2 4, y) 2. Translation: (x, y) m (x, y 1 2) Reflection: in the x-axis Reflection: in y 5 x

y y

1 x

The vertices of n ABC are A(3, 1), B(1, 5), and C(5, 3). Graph the image of n ABC after a composition of the transformations in the order they are listed. 3. Translation: (x, y) m(x 1 3, y 2 5) 4. Translation: (x, y) m (x 2 6, y 1 1) Reﬂection: in the y-axis Rotation: 908 about the origin

y y 1

21 x

} Graph F 0G0 after a composition of the transformations in the order they are listed. Then perform the transformations in reverse order. Does the } order affect the final image F 0G0 ? 5. F(4, 24), G(1, 22) 6. F(21, 23), G(24, 22) Rotation: 908 about the origin Reflection: in the line x 5 1 Reflection: in the y-axis Translation: (x, y) m(x 1 2, y 1 10)

y y

1 x Geometry 172 Practice Workbook Name ——————————————————————— Date ————————————

LESSON Practice continued 9.5 For use with the lesson “Apply Compositions of Transformations”

Describe the composition of transformations.

7. A B y 8. y A D C B D C C 1 1 B D C C 5 x 1 x B A A C B A B A

} } In the diagram, k i m, AB is reﬂected in line k, and A 9B9 is reﬂected in line m. } 9. A translation maps AB onto which segment? B

10. Which lines are perpendicular to BB@ ###$0 ? A9 k B9

} m 11. Name two segments parallel to AA0 . B99 A99

12. If the distance between} k and m is 2.7 centimeters, what is the length of AA0 ?

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. 13. Is the distance from A9 to m the same as the distance from A0 to m? Explain.

Geometry Practice Workbook 173 Name ——————————————————————— Date ————————————

LESSON Practice continued 9.5 For use with the lesson “Apply Compositions of Transformations”

Find the angle of rotation that maps A onto A0.

14. m 15. k k A9 m A99 A99

608 A 458 A9 A

16. Stenciling a Border The border pattern below was made with a stencil. Describe how the border was created using one stencil four times.

Geometry 174 Practice Workbook Name ——————————————————————— Date ————————————

LESSON Practice 9.6 For use with the lesson “Identify Symmetry”

Determine whether the ﬁgure has rotational symmetry. If so, describe the rotations that map the ﬁgure onto itself. 1. 2. 3. 4.

Does the ﬁgure have the rotational symmetry shown? If not, does the ﬁgure have any rotational symmetry? 5. 1208 6. 1808 7. 458

8. 368 9. 1808 10. 908

Geometry Practice Workbook 175 Name ——————————————————————— Date ————————————

LESSON Practice continued 9.6 For use with the lesson “Identify Symmetry”

In Exercises 11–16, draw a ﬁgure for the description. If not possible, write not possible. 11. A triangle with exactly two lines 12. A quadrilateral with exactly two lines of symmetry of symmetry

13. A pentagon with exactly two lines 14. A hexagon with exactly two lines of symmetry of symmetry

15. An octagon with exactly two lines 16. A quadrilateral with exactly four lines of symmetry of symmetry

17. Paper Folding A piece of paper is folded in half and some cuts are made, as shown. Which ﬁgure represents the piece of paper unfolded?

Geometry 176 Practice Workbook Name ——————————————————————— Date ————————————

LESSON Practice continued 9.6 For use with the lesson “Identify Symmetry”

In Exercises 18 and 19, use the following information. Taj Mahal The Taj Mahal, located in India, was built between 1631 and 1653 by the emperor Shah Jahan as a monument to his wife. The ﬂoor map of the Taj Mahal is shown. 18. How many lines of symmetry does the ﬂoor map have?

19. Does the ﬂoor map have rotational symmetry? If so, describe a rotation that maps the pattern onto itself.

In Exercises 20 and 21, use the following information. Drains Refer to the diagram below of a drain in a sink. 20. Does the drain have rotational symmetry? If so, describe the rotations that map the image onto itself.

21. Would your answer to Exercise 20 change if you disregard the shading of the figures? Explain your reasoning. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifflin Harcourt Publishing Company.

Geometry Practice Workbook 177 Name ——————————————————————— Date ————————————

LESSON Practice 9.7 For use with the lesson “Identify and Perform Dilations”

Find the scale factor. Tell whether the dilation is a reduction or an enlargement. Then ﬁnd the values of the variables.

1. 5 P C 2. 12 P 9 9 P 4 5 P x 6 C 6 x 12

Use the origin as the center of the dilation and the given scale factor to ﬁnd the coordinates of the vertices of the image of the polygon. 1 3. k 5 3 4. k 5 } 3

y y

N G M

H 1 2 I 1 L x 2 x

5 5. k 5 2 6. k 5 } 2

y R y D A C S 1

Geometry 178 Practice Workbook Name ——————————————————————— Date ————————————

LESSON Practice continued 9.7 For use with the lesson “Identify and Perform Dilations”

A dilation maps A to A9 and B to B9. Find the scale factor of the dilation. Find the center of the dilation. 7. A(4, 2), A9(5, 1), B(10, 6), B9(8, 3)

8. A(1, 6), A9(3, 2), B(2, 12), B9(6, 20)

9. A(3, 6), A9(6, 3), B(11, 10), B9(8, 4)

10. A(24, 1), A9(25, 3), B(21, 0), B9(1, 1)

The vertices of ~ABCD are A(1, 1), B(3, 5), C(11, 5), and D(9, 1). Graph the image of the parallelogram after a composition of the transformations in the order they are listed. 11. Translation: (x, y) m (x 1 5, y 2 2) 3 Dilation: centered at the origin with a scale factor of } 5

Geometry Practice Workbook 179 Name ——————————————————————— Date ————————————

LESSON Practice continued 9.7 For use with the lesson “Identify and Perform Dilations”

12. Dilation: centered at the origin with a scale factor of 2

Reﬂection: in the x-axis

y 4 x 22

In Exercises 13–15, use the following information. Flashlight Image You are projecting images onto a wall with a flashlight. The lamp of the flashlight is 8.3 centimeters away from the wall. The preimage is imprinted onto a clear cap that fits over the end of the flashlight. This cap has a diameter of 3 centimeters. The preimage has a height of 2 centimeters and the lamp of the flashlight is located 2.7 centimeters from the preimage. 13. Sketch a diagram of the dilation.

14. Find the diameter of the circle of light projected onto the wall from the ﬂashlight.

Use thediagramtodetermineifstatementis Use Name 1. 8. 7. 6. 5. 3. LESSON 10.1 Draw asecantandlabelit Draw adiameterandlabelit Supposethetwo circlesshown areinscribed Thecirclesintersectatthepoint(6,3). The lines Thedistancebetween thecentersofcirclesis ( is 36units. in arectangle. The perimeteroftherectangle common tangentsofthetwo circles. equal tothelengthofdiametereachcircle. ———————————————————————

P todrawthedescribedpartofcircle. P P For usewiththelesson”UsePropertiesofTangents” Practice y

5 0and

5 4representallthe EF } AB } .

4. 2. Draw achordandlabelit Draw atangentray andlabelit true

1 P P or y 1 false A Date . ———————————— GH } B

. Practice Workbook CD # ## $ .

Geometry x

181 182 Name The points In Exercises12–17, 9. Draw twocirclesthathavethegivennumberofcommontangents. Find thevalueof 18. 15. 12. Practice Workbook Geometry LESSON 10.1

3 ——————————————————————— C LJ C x B M K x For usewiththelesson“UsePropertiesofTangents” Practice K 16 x and A B 32 100 96 4 7 x x x M

. 1 2 arepointsoftangency. Findthevalue(s)of BC } 7 8 isaradiusof

A continued

16. 13. 10. 19. 2

J A 3 x ( 2 x C

B 2 17 and 10 108 x x 56 AB } M K 32 B istangentto

45 L A C

11. 20. 17. 14. Date 0

( A 2

C x x . . 2 ————————————

C 48 J 3 x B 2 49 63 x 80 3 M A x K L B x C

nearest tenth. h aiso h wmigpo? 4000miles.Roundyour answer tothe theradiusofswimming pool? ntepo s4 eta hw.Wa s thehorizon? isabout The radiusofEarth onthepoolis48feetasshown. What is itnefo o oapito agny Whatisthedistance distancefromyou toapointoftangency rmacrua wmigpo.Te orbitingabout180milesabove Earth. fromacircularswimming pool. The in theﬁgure. asshown32 feetfromapointoftangency onthegreen Your and golfballis8feetfromtheedgeofgreen Golf In Exercises23and24,usethefollowinginformation. Name 24. 23. 21. LESSON 10.1

How isyour far golf ball fromthecupatcenterofgreen? Swimming Pool Assuming the green isﬂat,whatAssuming thegreen isradiusofgreen? A green onagolfcourseisintheshapeofcircle. A green ——————————————————————— For usewiththelesson“UsePropertiesofTangents” Practice r r 48 ft You arestanding36feet 36 ft continued

22. Space Shuttle d Supposeaspaceshuttleis Date 180 mi ———————————— d fromtheshuttleto Practice Workbook 8 ft 32 f Geometry t

183 184 In theﬁgure, In Name or

indicated arc. 11. 17. 15. 13. 3. 9. 7. 5. 1. Practice Workbook Geometry ( semicircle LESSON 10.2

F m m m m m BAE C CAD C EAC C AB C , determinewhetherthegivenarcisa ——————————————————————— PS C PQS C RQS C TPS C PQ C

For usewiththelesson“FindArcMeasures” Practice . PR }

and QS } 14. 12. 10. 18. 16. 8. 6. 4. 2. arediametersof DEC ACD DEB AE m m m C C C C m m QR C RT C ST C PTR C TQR C

( U minor arc . Findthemeasureof T E P D A , 64 major arc S 8 F 42 U 8 Date B R , ———————————— C

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. if if Two diameters of Two diametersof Find theindicatedarcmeasure. PQ C Name 21. 28. 24. 19. m m LESSON 10.2

hasameasureof90

JM C PR C m m m C ——————————————————————— JL C PS C AC C

5 5 R

A 165 35 D For usewiththelesson“FindArcMeasures” Practice 8 . 8 . B

( ( N T are are 29. 25. 8 in PQ } JK } continued m m ( PSR C JMK C

and and

R 22. . Findthelengthof

LM } RS } m ACB C .Findthegivenarcmeasure C A

.Findthegivenarcmeasure

20. 30. 26. B

P m m JLM C PRQ C PQ } 10

R 23. Date

A m DAB C B ———————————— 31. 27.

E m m KLM C PRS C C Practice Workbook D

Geometry 185 186

Sprinkler In Exercises39and40,usethefollowinginformation. sections. Findthemeasureofeacharc. Game Shows Tell whetherthegivenarcsarecongruent. Name It moves throughthecovered areaatarateofabout5 34. 40. 39. 36. 32. Practice Workbook Geometry LESSON 10.2 If the sprinkler starts at the far leftposition, atthefar Ifthesprinkler starts Whatisthemeasureofarccovered by thesprinkler?

EF JK J the far rightposition? the far how longwillittake forthesprinklertoreach C C ——————————————————————— E

and 4 and Awater sprinklercovers theareashown intheﬁgure. 105 75

For usewiththelesson“FindArcMeasures” Practice M QR C GH C 8 8 Eachgameshowwheelshownisdivided intocongruent

K H G 37. 75 8 P 4.5 R 105 continued

35. 33. o persecond.

S B STV C AB C A T 30

and 42

and 8 96 8

8 CD C

C UVT C 180 38.

8 V U

D Date

5 8 ————————————

Find thevalueof Find themeasureofgivenarcorchord. Name 10. 1. 7. 4. LESSON 10.3

C V m m 3 13 ——————————————————————— A x S 7 C AC AC C BC C

1 1 16 18

4 A

18 6 D x For usewiththelesson“ApplyPropertiesofChords” Practice x D 7 E

W 130 2 F 5 J U 8 116 B B T

8 .

G 12 x

1 7

11. 8. 5. 2.

M 12 S x m m 12 D JK

A M 1 PQR C LM C J 9 N

U L 3

x K

E P 2 T N C 11 3 L 7 40 x x

B 1 R

8 2

6 10

12. 6. 3. 9. Date

Y m QS } 38 9 x M P J KLM C 8

S 2 ————————————

11 3 V P Z T

142 X R N 14 8 x Practice Workbook T

9 W 2 L S x K 9

1 R 21 7 Geometry x

1 5 187 188

7. determinewhether In Exercises13–16,

Name 15. 17. 13. Practice Workbook Geometry LESSON 10.3

P Statements GIVEN: PROVE: 6. 5. 4. 3. 2. 1. Proof ——————————————————————— S AD ? C ? n AE } DE } ? AC } P 8 AED Completetheproof.

is adiameterof > > > For usewiththelesson“ApplyPropertiesofChords” Practice R 8

AE } AB C

BE } AC } AD C

S ù

is adiameterof n

ù R AEB

AB C

( F continued . AC } (

> F

. BD } } AC

BD } PR }

isadiameterofthecircle.

16. 14.

D P Reasons 7. 6. 5. 4. 3. 2. 1. ? triangles ofcongruent parts Corresponding ? ? ? All rightangles arecongruent. ? are congruent. F E R C A S P B S R Date ————————————

Name

19. 18. LESSON 10.3 Brieﬂy explain what other congruence postulateyou Brieﬂyexplain whatcouldusetoprove othercongruence that Statements PROVE: n GIVEN: 4. 3. 2. 1. Proof ———————————————————————

PUT PQ ? n UP } ? }

PUT isadiameterof Completetheproof.

For usewiththelesson“ApplyPropertiesofChords” Practice ù

UQ } PQ }

n n ù

PUT

QUS

is adiameterof ù

QUS UT }

inExercise 18. ù

n ù

QUS ( US }

continued . PT C (

ù U .

QS C PT C

QS C

P Reasons 4. 3. 2. 1. T ? ? Theorem 10.3 ? U S Date ———————————— Practice Workbook Geometry 189 190

Find themeasureofindicatedangleorarcin 5. 2. Find themeasureofindicatedangleorarcin Name

given

10. 14. 12. 8. 1. Practice Workbook Geometry LESSON 10.4

S m m m Multiple Choice m m m C. A. A D ——————————————————————— m MJ C ST C

54 61 LM C

KLN KMN JKL A E P 3. 8

6. 8 RPS SPR For usewiththelesson“UseInscribedAnglesandPolygons” Practice T B

84 U C > >

8 and PRQ PSQ Intheﬁgureshown, which statementistrue? m

KN C

5 116 15. 13. 11. D. B. 9.

8 M m m m m m m . A J LKJ C AB C PRQ RQS LNM JKM MKL K 20 4. B

P 8 > > 28

8 C RPS SQR

K L

( ( P P , .

7. J Date

S M 39 m m J V VST C N 8 P ———————————— S JLM P K 88

8 R 51 U P 8 K L M T 135 8 L

22. 19. 16. LESSON 10.4

M (4 Multiple Choice C. A. ——————————————————————— y 16 7 104 2 J 5 1) x

8 L 8 For usewiththelesson“UseInscribedAnglesandPolygons” Practice P 8 2 S 63 y 110 8 8 K 8 3 17. x 65 R 8 What isthevalue of 8 20. continued D. B. 21 12 S 84 8 D T 64 A x 2 intheﬁgureshown? 7 8 x 80 y 8 8 8 4 B y 64 8 C U 8 V 4 152 18. x 8 8 21.

Date B A P 96 5 8 x ———————————— E S 8 y H 108 8 48 3 C 45 8 y 8 8 8 F x (9 G 8 12 x R 1 x Practice Workbook 8 21) 8 Geometry 191 192 Name

25. 24. 23. Practice Workbook Geometry LESSON 10.4 5. 4. 3. 2. 1. 4. 3. 2. 1. GIVEN: PROVE: GIVEN: PROVE: Proof Name two otheranglesthatcouldbeusedinStep3ofExercise 23. Proof Statements Statements ——————————————————————— ? ? ? n AB C n ( P BDC CAD ABE AED Completetheproof. Completetheproof.

> For usewiththelesson“UseInscribedAnglesandPolygons” Practice

CD C

( AB C n n

> ù > ,

P AED ABE

> DCE BEC CAB DBC

CD C

> ,

n DCE BEC continued

5. 4. 3. 2. 1. Reasons Reasons 4. 3. 2. 1. ? ? Vertical Angles Theorem 10.3 Theorem ? ? ? Vertical AnglesTheorem Given

A A D D P E E B B C C Date ————————————

7. Find Find theindicatedarcmeasure. Name 10. 1. 4. LESSON 10.5

174 248 m m C ——————————————————————— AB C 1 8 8 1. 1

B For usewiththelesson“ApplyOtherAngleRelationshipsinCircles” Practice A 101 8 1

119

243 8 8

11. 8. 5. 2.

G 116 m FH C 120 1 8 1 98

8 8 H 129 138 1

8 8 F 140

12. 6. 3. 9. Date

K 108 m 53 JKL C 8 ———————————— 1 8 L

104 104 1 8 8 J 34 Practice Workbook 8 41 1 8 111 Geometry 8 193 194 measuresofallthenumberedangles. tothecircleatpoint Use thediagramshowntoﬁndmeasure ﬁndthevalueof In Exercises13–18, Name of theangle. 24. 22. 20. 19. 16. 13. Practice Workbook Geometry LESSON 10.5 shown, Inthediagram

(10 m m m x ——————————————————————— 8 x CAF DCF CEF 1

1) For usewiththelesson“ApplyOtherAngleRelationshipsinCircles” Practice 129 8

8 (5 x 35 2

1) 25. 23. 21. 8 m 61 S istangent 8 . Find the continued m m m

17. 14. BCD CFB AFB

39 x 24 . 8 (7 8 x 2 x

2) 8 110 (17 8 AE B 118 V x U 1 4 8

70 6) 3 2 W 8 8

18. 15. S 1 F C T Date

124 (13 25 8 x 8 ———————————— 120 D m 2 137

8 6) 8 8

(5 x 1

14) x 8 8 54 8

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. see? isabout4000miles. The radiusofEarth ofabout7milesabove Earth. What isthemeasure of arc In Exercises26and27,thecirclesareconcentric.Findvalueof Name 28. 29. 26 LESSON 10.5

Transportation measure of the arc that represents the part of Earth themountainclimbercansee. ofEarth measure ofthearcthatrepresentspart about 4.75milesabove sealevel. fromExercise Usetheinformation 28toﬁndthe Mountain Climbing ——————————————————————— 32 TV 8 For usewiththelesson“ApplyOtherAngleRelationshipsinCircles” Practice that represents the part of Earth you ofEarth can thatrepresentsthepart x 8 Aplaneisﬂyingatanaltitude 96 A mountainclimber isstandingontopofamountainthat 8

continued 27.

4007 mi 124 8 167 W x 8 Date 8 T ———————————— U x . V Not drawntoscal Practice Workbook 4000 mi Geometry e

195 196 Find thevalueof Find Find thevalueof Find Find thevalueof Name 13. 10. 7. 4. 1. Practice Workbook Geometry LESSON 10.6

A RT AB ——————————————————————— R 5 315 23 x and x and

10 1 D 23 1 10 x 5 For usewiththelesson“FindSegmentLengthsinCircles” Practice 3 x x 12 2 x x TV 3 DE ST 6 V B 8 . 2. U . 2 3 E 10 5. 8. x x x 14. 11. . . .

DE T x x 21 x 6

A 1

9 1 x 10 x 13 27

U 3 4 1 3 1 x S x 7 5 2 4 B x x 6. R 1 9. V 8 15. 12. 3. Date

x R

A 6 ———————————— E 6 V 10 5 4 x x 12 x x D x

3 x 1 x x

U 4 6 9 12 x S 15 20 B 15 T

x 3 PQ S ——————————————————————— 3 4 x 1 2 . 3 15 2 2 3 x For usewiththelesson“FindSegmentLengthsinCircles” Practice x x x 2 1 R 1 6

P 1 2 12 x x x x 20. . 26. 2 17. x 2 4 23. continued

R x x 2 1 36 24 10 42 S 2 2 x x 2 x 20 x 8 5 3 x 21. 24. P 27. 18. Date

2 x ———————————— R x x 8 48 N 2 28 21 2 5 x x x 70 1 Practice Workbook x 5 1 Geometry P 197 198 Name 30. 29. 28. Practice Workbook Geometry LESSON 10.6 inch, whatdrainpipe? isthediameterofstorm the water is4.25inches deepatitsdeepestpoint. To thenearest ofthewaterThe distanceacrossthesurface is48inchesand drainpipewithasmallamountofstandingwater.storm Basketball Storm Drain Winch to thespoolis8inches. What isthediameterofspool? winch’s spoolandthedistancefromendofcable There are15inchesofthecable hangingfreeoff ofthe long isthepass? player onthekey. To thenearesttenthofafoot,how court. The player outsidethekey passestheballto teammates relative tothecircular“key” onabasketball ——————————————————————— Alarge industrialwinchisenclosedasshown. For usewiththelesson“FindSegmentLengthsinCircles” Practice The The diagram shows Thediagram across-sectionof large X s show thepositionsoftwo basketball continued

Date 4.25 in. ———————————— 12 ft 5 ft 8 in. 48 in. 15 in. 6 ft

Use thegiveninformationtowritestandard equationofthecircle. Write thestandardequationofcirclewithgivencenterandradius. Write thestandardequationofcircle. Name 12. 11. 9. 1. 7. 5. 3. LESSON 10.7

Thecenter is(0,0),andapointonthecircle(3, Thecenteris(0,0),andapointonthecircle(4,0). Center(0,14),radius14 Center ( Center (0,0),radius9 ——————————————————————— For usewiththelesson“Write andGraphEquationsofCircles” Practice 2 2 1 3, 0),radius5 y y 2 1 x x 10. 4. 2. 8. 6. 2 Center ( Center (4, Center (1,3),radius4 4). 1 y 1 2 2 12, 7),radius6 2 y 7), radius13 2 Date ———————————— x x Practice Workbook Geometry 199 200

Graph theequation. Determine thediameterofcirclewithgivenequation. Name 19. 16. 15. 14. 21. 17. 13. Practice Workbook Geometry LESSON 10.7 ( Thecenteris(17,24),andapointonthecircle( Thecenteris( Thecenteris(3, Thecenteris(2,4),andapoint onthecircleis( x x ——————————————————————— x 2 2

2 1 1 2)

y y 2 2 For usewiththelesson“Write andGraphEquationsofCircles” Practice 2

5 5 1 100 64 ( 2 y

2 2 y 2 43, 5),andapointonthecircleis( 9) 2 2), andapointonthecircleis(23,19). 2

5 4 continued x

22. 20. 18. 2 3, 16). 2 ( ( ( 2 3, 9). x x x 34, 17). 1

2 1 2 y 4) 16) 12) 1 2

2 2 1

1 1 ( ( ( y

y y 1

Date 1 1 1) 15) 5) 2

———————————— 2 5

2 5

16 5 64 81 x

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. ( Determine whetherthepointliesoncircledescribedbyequation Name

23. 28. 27. x

2 LESSON 10.7 (0, 0)

3) b. b. locations, where thecoordinateunitsaremiles. Earthquakes Olympic Flag At At At same row is3inches. the distancebetween any two adjacentringsinthe In additiontothedimensionsshown inthediagram, for anOlympicprogram todesignapattern ﬂag. c. a. a. ——————————————————————— 2 Eachring is3inchesthick. Whatarethecoordinatesofepicenter? Graphthreecirclesinonecoordinateplane C B A

equations representingthe inner circles. adjust theequationsofoutercirclestowrite bydetermined eachoftheseismograph readings. to representthepossible epicenterlocations the lower oftheﬂagatorigin. left corner Use inchesasunitsinacoordinateplanewith representing theoutercirclesofﬁve rings. Use thegiven dimensionstowriteequations People upto9miles from couldfeeltheearthquake its epicenter. Couldapersonat(4, Explain 1 ( (2, 1),theepicenteris5milesaway. ( 2 2 ( For usewiththelesson“Write andGraphEquationsofCircles” Practice y 2, 6, 4),theepicenteris4milesaway.

2 2 . 8) 2), theepicenteris6milesaway. After an earthquake, you Afteranearthquake, aregiven seismograph readingsfromthree 2 You areusingamathsoftware

5 100. 24. continued (13, 8) Explain 2 how you can 5) feelit?

25. ( 2 5, 2) 15 in. Date 18 in. ———————————— 26. 2 y (11, 5) 2 26 in. 31 in. Practice Workbook x Geometry

201 202 Find thelengthof Find theindicatedmeasure. Use thediagramtoﬁndindicatedmeasure. Name

8. 5. 7. 6. 4. 1. Practice Workbook Geometry LESSON 11.1 Theexact circumferenceofacirclewithradius27feet Theexact radiusofacirclewithcircumference42meters The exact circumferenceofacirclewithdiameter15inches The exact diameterofacirclewithcircumference39centimeters Find thecircumference. ——————————————————————— 6 cm P For usewiththelesson“CircumferenceandArcLength” Practice 60 8 ft A

AB C

. 9. 2. Find thecircumference. A 150 13 in. 18 in. B P

3. 10. Date

C Find theradius. C

5 ———————————— 65.98cm 30 P 28 ft r A B

Find theperimeterofregion. Find theindicatedmeasure. In Name

20. 17. 14. 11. ( LESSON 11.1 Lengthof

D 7 m m m ——————————————————————— shownbelow, H D

AB C EFG C F 80 12 in. C

B For usewiththelesson“CircumferenceandArcLength” Practice

5 mm G EHG C

A 23.88 in.

EDF

continued

18. 15. 12. FDG 46.75 ft m m Circumference of . Findtheindicatedmeasure.

EHF C EHG C

290 21. F

11 in. ( E D F

16. 13. 19. Date 19.71 cm Length of Length of Radius of 41 in. 41 in. ———————————— G H ( FEG C EFG C 55 J Practice Workbook

J Geometry 11 in 203 204 Name 22. 24. 23. Practice Workbook Geometry LESSON 11.1 Inthetable below, b. 160 much fencingdoyou need? ofyour garage,asshown.corners You want tofenceinyour garden. About how Enclosing aGarden The circumferenceofeachsprocket isgiven. Bicycles a. ——————————————————————— Length of m Radius Onachain,theteetharespacedin Abouthow longisthechain? rear sprocket there onthischain?

AB C C

5 For usewiththelesson“CircumferenceandArcLength” Practice

12in. 12 ft The chainofabicycle travels alongthefrontandrearsprockets, asshown. AB C

10 in. 10 in. AB C You have plantedacirculargardenadjacenttooneofthe 30

referstothearcofacircle.Completetable. 19510.7 9.5 11 4 8 front sprocket continued C

5 .61.46314.63 6.3 17.94 8.26 20in. 105 } 2 1 185

inchintervals. About how many teethare 8 75 8 270 8 Date ————————————

Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Find theareasofsectorsformedby Find theindicatedmeasure. nearest hundredth. Find theexactareaofcircle.Thenfindto Name 8. 5. 4. 1. 7. 6. LESSON 11.2 Theareaofacircleis173squareinches.Find theradius. Theareaofacircleis528squarefeet.Find thediameter.

The areaofacircleis654squarecentimeters.Find thediameter. The areaofacircleis290squaremeters.Find theradius. D ——————————————————————— 4 in. C For usewiththelesson“AreasofCirclesandSectors” Practice 65 6 in. A

9. 2.

130 A 10.5 ft B 27 cm ACB C 3. . D

10. Date

B D ———————————— 24.8 cm 209 C 18 m Practice Workbook A

Geometry 205 206 Find theareaofshadedregion. 55 squareinches.Findtheindicatedmeasure. The areaof Use thediagramtoﬁndindicatedmeasure. Name

23. 20. 18. 16. 14. 11. Practice Workbook Geometry LESSON 11.2 Perimeter ofshadedregion Radius of Find theareaof G H m ——————————————————————— 6 cm

PQ C A 10 ft

23.79ft For usewiththelesson“AreasofCirclesandSectors” Practice ( 43 (

R 80 is295.52squareinches.Theareaofsector R 2 ft

E 2 F (

. continued 24. 21. 19. 17. 15. 12. Perimeter ofunshadedregion Lengthof Circumference of Find theradiusof G A

5 40.62in. H 6 in. 98 13 in. PQ C F E 2

25.

( ( R H . 13. 22. PRQ Date

T E Find thediameterof F is

A ————————————

51 5 R 31.47m 9 m H P 3.5 m G 2 8 cm

( H .

b. water sprinkler. Landscaping the glassinshadedregion. Window Design the fountain. Fountain a. ——————————————————————— Thewater pressureisweakened sothattheradiusis10feet. What istheareaof Whatistheareaoflawn thatiscovered by thesprinkler? lawn thatwillbecovered? For usewiththelesson“AreasofCirclesandSectors” Practice 3 m A circularwater fountainhasadiameterof42feet.Find theareaof 16 ft 45 The diagram attherightshowsThe diagram theareaofalawn covered by a 3 m Thewindow shown isintheshapeofasemicircle.Find theareaof 135 continued Date ———————————— Practice Workbook Geometry 207 208 Find thegivenanglemeasureforregulardodecagonshown. if necessary. number ofsides.Roundanswerstothenearesttenthadegree, Find themeasureofacentralangleregularpolygonwithgiven Name

13. 12. 11. 9. 7. 5. 1. Practice Workbook Geometry LESSON 11.3 Aregular octagonhasdiameter 8.5feet. What isthelengthofitsapothem? Aregular hexagon hasdiameter 22inches. What isthelengthofitsapothem? A. C. Round your answer tothenearesttenth. Round your answer tothenearesttenth. side length10.5? Multiple Choice m m m 20 sides ———————————————————————

UWK XUW TWU a a

5 5 For usewiththelesson“AreasofRegularPolygons” Practice

} } tan 20 tan 40 6. 8. 10. 5.25 5.25

8 8

Whichexpression gives theapothemforaregular nonagonwith 2. 36 sides m m m XWK TWK TWX

D. B. 3.

T a a 120 sides S X

5 5 U R 5.25 } tan 20 V 10.5 W 4. +

J P 8 tan20

K N Date M L 8

———————————— 23 sides

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. nearest tenth,ifnecessary. Find theperimeterandareaofregularpolygon.Roundanswersto Name

24. 23. 22. 21. 20. 17. 14. LESSON 11.3 Whatistheareaofaregular 18-gonwithasidelengthof8meters?Roundyour Find theareaofaregular octagon inscribedinacirclewhose equationisgiven by Find theareaofaregular pentagoninscribedinacircle whose equationisgiven by Whatistheareaofaregular 30-gonwitharadiusof20feet?Roundyour answer Whatistheareaofaregular 24-gonwithasidelengthof10inches?Roundyour

answer tothenearesttenth,ifnecessary. ( ( to thenearesttenth,ifnecessary. answer tothenearesttenth,ifnecessary. ——————————————————————— x x

2 2 2) 4) 4.5 For usewiththelesson“AreasofRegularPolygons” Practice 2 2 1 1 8 ( ( y y

1 2 3) 6) 2 2

5 5 25. 16. continued 18. 15. 20

19. 16. Date

———————————— 2.5 5 Practice Workbook Geometry 209 210 regular hexagons asshown. Tiles In Exercises29and30,usethefollowinginformation. if necessary. Find theareaofshadedregion.Roundanswerstonearesttenth, Name

27. 31. 30. 29. 25. Practice Workbook Geometry LESSON 11.3 A cup saucer is shaped like a regular decagon with a Acupsaucerisshapedlike aregular decagonwitha Thehallway hasawidthof5feetandlength12feet. Whatistheareaofeachtile?

You aretilingtheﬂoorofahallway withtilesthatare b. At leasthow many tileswillyou need? diameter of5.5inchesasshown. a. ——————————————————————— Whatistheperimeterandareaof thesaucer?Round Whatis thelengthofapothemsaucer? your answers tothenearesttenth. Round your answer tothenearesttenth. 40 16 For usewiththelesson“AreasofRegularPolygons” Practice 12

continued 28. 26.

10 72

16 Date ———————————— 5.5 in. 6 in.

Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. given segment.Expressyouranswerasafraction,decimal,andpercent. satisfies theinequality. Find theprobabilitythatapointchosenatrandom onthesegment shaded region. Find theprobabilitythatarandomlychosenpointinfigurelies Find theprobabilitythatapoint Name 11. 123456789 1. 8. 5. LESSON 11.4

C E D C A B 8 x BC } ———————————————————————

3 6 b For usewiththelesson“UseGeometricProbability” Practice 8 16 5 4 6 2

12. 2. 02468

2 BD } x

3 9. 6. K b 3 , selectedrandomlyon 12 06 10 13. 3. 4

3 CE } x

8 5 6 2 r

17 AE } 10. 7. ,isonthe

Date ———————————— 14. 4.

2 AD } 6 7 x

Practice Workbook 12 r 8 Geometry 211 212 with asectorthatinterceptsanarcof60°.

shaded region. Find theprobabilitythatarandomlychosen pointintheﬁgurelies Arcs andSectors In Exercises19and20,usethefollowinginformation. Use thescaledrawing. Name

17. 16. 21. 20. 19. 18. 15. Practice Workbook Geometry LESSON 11.4 Find theprobabilitythatarandomly chosenpointinthe Find theprobabilitythatarandomly chosenpointon Find theprobabilitythatarandomly chosenpoint Find theprobabilitythatarandomly chosenpoint Whatistheapproximate areaoftheshadedﬁgure in thescaledrawing? circle liesinthesector. the circleliesonarc. the balllandsinbucket. a two footcubicbox. A smallballisthrown into thebox. Find theprobabilitythat Boxes andBuckets lies outsideoftheshadedregion. lies intheshadedregion. ——————————————————————— 12 For usewiththelesson“UseGeometricProbability” Practice Theﬁguretotherightshows acircle 8

Acircularbucket withadiameterof18inchesisplacedinside continued 22. 44 2

23. Date 1.5 6 ———————————— 60

Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. fire drillscheduledtohappenatarandomtimeduringtheday. Lunch is25minutes. Transfer timebetween classesand/orlunchis3minutes. There isa School Day usethefollowinginformation. In Exercises26–28, Name 28. 27. 26. 25. 24. LESSON 11.4

Ifyou are2hourslatetoschool,what istheprobabilitythatyou missedthe Whatistheprobabilitythatfiredrillbegins duringtransfer time? Whatistheprobabilitythatfiredrillbegins duringlunch? A. C. a pedestrianarrives atthestationarandomtime? forthenext station. departs What istheprobabilitythatthereatrainwaiting when 15 minutes. The trainwaits for2minuteswhile passengersgetoff andon, then Subway Multiple Choice fire drill? What istheprobabilitythat region B. ———————————————————————

}} }}} }} Area of Area of Area of Theschoolday consistsofsixblock classeswitheachbeing60minuteslong. A For usewiththelesson“UseGeometricProbability” Practice Atthelocalsubway station,asubway trainisscheduledtoarrive every , and Area of Area of Area of A A A

A 2 1 1 includesregion Area of Area of Area of Area A point A A A

1 Area of Area

B C C

2 continued X Area of Area X ischosenatrandomin isnotin C

andregion

B ? C .

A B C Date ———————————— Practice Workbook Geometry 213 214 Egs de:2 Edges: Edges: 24 Edges: 6 Vertices: Vertices: 4 Sketch thepolyhedron. Use Euler’s Theoremtoﬁndthevalueof Explain Determine whetherthesolidisapolyhedron.Ifitis,name Name 7. 4. 1. Practice Workbook Geometry LESSON 11.5 Triangular pyramid Faces: ——————————————————————— yourreasoning. n For usewiththelesson“ExploreSolids” Practice

8. 5. 2. Faces: 10 Pentagonal pyramid n n . Vertices: 24

3. 9. 6. Date Hexagonal prism Faces: 14 ———————————— n

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Determine whetherthesolidis Check youranswerusingEuler’s Theorem. Find thenumberoffaces,vertices,andedgespolyhedron. Name 17. 16. 13. 10. LESSON 11.5

of thebuilding? shape ofapyramid. The buildingwillhave eightsides. What istheshapeofbase Visual Thinking ——————————————————————— For usewiththelesson“ExploreSolids” Practice An architect is designing a contemporary ofﬁcebuildinginthe Anarchitectisdesigningacontemporary

continued 18. 14. 11. convex

or concave .

15. 12. 19. Date

———————————— Practice Workbook Geometry 215 216 Cross Section usethefollowinginformation. In Exercises25–27, and thesolid. Describe thecrosssectionformedbyintersectionofplane Name

ofthe cube. through threevertices is intersectedby adiagonalplane. The crosssectionpasses 27. 26. 25. 24. 23. 20. Practice Workbook Geometry LESSON 11.5 Iftheedge lengthofthecubeis4 Iftheedgelengthofcubeis1,what isthelength Whattypeoftriangleistheshapecrosssection? D. A. C. B. of thelinesegment Howcombination hasthemostfaces? many arethere? faces Reasoning a hexahedron? ofanothersolid. face Which two toform faces solidscanbeadjoinedby congruent Multiple Choice perimeter ofthecrosssection? ——————————————————————— Acubeandatriangularprism Atriangularprismandapyramid Atriangularpyramid andatriangularpyramid Arectangularprismandapyramid For usewiththelesson“ExploreSolids” Practice Theﬁgureattherightshows acubethat Ofthefourpossible solidcombinationsinExercise 23,which Assume at least one face of a solid is congruent toatleastone ofasolidiscongruent Assumeatleastoneface d ? continued

21. Ï } 2 , what isthe

22. Date ———————————— d

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. 4. two decimalplaces. Find thevolumeofrightprismorcylinder. Roundyouranswerto contained inthesolid. Find thevolumeofsolidbydetermininghowmanyunitcubesare Name 1. 6. LESSON 11.6

5 6 m ——————————————————————— 8 cm For usewiththelesson“Volume ofPrismsandCylinders” Practice 4 8 m 9 3 5 cm 5

4 m 4 2

2. 3 3 2 10 7. 5. 2

2 7 4 ft 3 ft 3 5

9 in. 3. Date 4 ———————————— 3 6 3 2 7 in. 3 in. Practice Workbook 10 7 Geometry 2 5 217 218

decimal places. Sketch thedescribedsolidandﬁnditsvolume. Roundyouranswertotwo Find thelength Name

it f6fe,adlnt f9fe. aheightof8meters. widthof6feet,andlength9feet. 13. 14. 10. 8. Practice Workbook Geometry LESSON 11.6 Arectangularprismwithaheightof3feet, 5 in. 10 incheslong,8wide,and4tall? Multiple Choice V A. ———————————————————————

5 4 24 1440m For usewiththelesson“Volume ofPrismsandCylinders” Practice 15 m 3 x

12 in. usingthegivenvolume How many 2 inchcubescanﬁtcompletely inabox thatis

x continued B. 32 8 m 11. C.

5 360ft 17 ft V . 3

15. 9. Arightcylinder witharadiusof4metersand 2 cm 0 40 8 ft x

12. Date 22 cm V 2 cm

5 ———————————— 72 Ĭ D. cm x 320 3

Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 12 inches.Roundyour answers totwo decimalplaces. hexagonal widthof2inchesandaheight prismswith a face pillars outofplasterparis. The pillarswillbeshapedasregular Pillars usethefollowinginformation. In Exercises21–23, 18. cylinder. Roundyouranswertotwodecimalplaces. Use Cavalieri’s Principletofindthevolumeofobliqueprismor Round youranswertotwodecimalplaces. Find thevolumeofsolid.Theprismsandcylindersareright.

Name 23. 22. 21. 16. LESSON 11.6

Is480cubic inchesenoughplasterofparisforallfourpillars? How muchplasterofparisisneededforonepillar? Whatistheareaofbaseapillar?

4 mm ——————————————————————— Inordertomodelahome,you needtocreatefour miniature 4 mm 4 mm For usewiththelesson“Volume ofPrismsandCylinders” Practice 3 mm 5 mm 6 mm 6 mm

3 mm continued

19.

5 in. 17. 2 in.

2 in. 7 in.

20. Date

2 in. 12 in. ———————————— 6 cm 5 in.

4 cm Practice Workbook Geometry 219 220 Find thevalueof Find thevolumeofsolid.Roundyouranswertotwodecimalplaces. Name 7. 4. 1. Practice Workbook Geometry LESSON 11.7

11 m V ———————————————————————

5 64in. x 6 cm 8 in. For usewiththelesson“Volume ofPyramidsandCones” Practice 4 cm 3

6 m x . 4 in.

8. 5. 2. V 9 in.

5 4 in. 147 x 5 in. 7 in. Ĭ 9 cm cm 3

3 in. 6 in.

6. 3. 9. Date V 4 cm 6 m

5 ———————————— 56m 5 cm 3 x 8 cm 4 cm 10 m 4 cm

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Round youranswertotwodecimalplaces. Find thevolumeofsolid.Theprisms,pyramids, andconesareright. 11. decimal places. Find thevolumeofrightcone.Roundyouranswertotwo C. Name 14. 10. LESSON 11.7

Multiple Choice What isitsradius? A. 6 m ——————————————————————— t 4ft t 2ft 8 m 18 cm For usewiththelesson“Volume ofPyramidsandCones” Practice 8 m 5 m Arightconehasaheightof6feetandvolume of32 60

continued 12.

D. B. 32 3ft 5ft 15.

13 m 7 in. 2 in.

13. Date

5 in. Ĭ ———————————— cubicfeet. 22 ft 6 ft 26 ? Practice Workbook Geometry 221 222 12 feethigh. The contractorhasaconicalpileofconcretemixthat measures22feetindiameterand Concrete usethefollowinginformation. In Exercises21–23, Name 18. 16. 23. 22. 21. 20. Practice Workbook Geometry LESSON 11.7 Does thecontractorhave enoughconcretetoﬁnishthejob? How many cubicyardsofconcreteare available tothecontractor? How many cubicfeetofconcreteareavailable to thecontractor? of thepyramid? 16 cubicfeet. The heightissixtimesthebaseedgelength. What istheheight Height ofaPyramid n 3in. 2 in. ——————————————————————— To job,acontractor needs78cubicyardsofconcrete. completeaconstruction For usewiththelesson“Volume ofPyramidsandCones” Practice 6 in. 6 cm 6 cm 6 cm 9 in. A rightpyramid withasquarebasehasvolume of continued 19. 17. 4 cm 6 mm 6 mm 6 cm 2 mm Date 6 mm 4 cm ———————————— 6 mm 6 cm 4 cm

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. its circumferenceis7 In Exercises5–7,usethespherebelow. Thecenterofthesphereis decimal places. Find thesurfaceareaofsphere.Roundyouranswertotwo Name 7. 6. 5. 1. 8. 4. LESSON 11.8

Find areaofonehemisphere. thesurface Find thediameterofsphere. Find theradiusofsphere. 40 Multiple Choice is the surface areaofthesphere? Roundyouris thesurface answer totwo decimalplaces. Great Circle Round your answer totwo decimalplaces. A. ——————————————————————— Ĭ t 2ft squarefeet? For usewiththelesson“SurfaceAreaandVolume ofSpheres” Practice The circumference of a great circleof a sphereis24.6 Thecircumferenceofagreat Whatistheapproximate areaof radiusofaspherewithsurface Ĭ centimeters. 4 cm B.

3.16ft

2. C. .2f 6.32ft 2 3 in.

3. Date Ĭ meters. What C ———————————— C and D. 10ft Practice Workbook 14 m Geometry 223 224 16. are right.Roundyouranswertotwodecimal places. Find thesurfaceareaandvolumeof solid.Thecylindersandcones to twodecimalplaces. Find theradiusofspherewithgivenvolume 9. Find thevolumeofsphere.Roundyouranswertotwodecimalplaces. Name 15. 12. Practice Workbook Geometry LESSON 11.8

128 Multiple Choice V A. ———————————————————————

5 . m 2.5cm Ĭ 64in. cubiccentimeters? For usewiththelesson“SurfaceAreaandVolume ofSpheres” Practice 3

6 cm 4 cm Whatistheapproximate radiusofaspherewithvolume of

7 ft continued B.

4.58cm 13. 17. 10.

5 C. 150 Ĭ cm 9 in. 3

.2c 6.62cm V 2 9 yd . Roundyouranswer 3 in. 14.

11. 18. Date

5 ———————————— 152m D. 3 8cm 17 ft 16 m 6 ft

Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Copyright © Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. Golf Balls usethefollowinginformation. In Exercises24–26, Complete thetablebelow. Leaveyour answersintermsof Name that they touchthelateralsidesandbasesofbox. are oftensoldinabox offour. Assume thattheballsarepacked tightly so 26. 25. 24. 22. 21. 20. 19. 23. LESSON 11.8

Whatis theamountofvolume insidethebox thatis nottaken upby the golfballs? Whatisthevolume ofagolfball? areaofagolfball? Whatisthesurface diameter ofthesphere? Finding aDiameter ——————————————————————— Radius ofsphere Astandardgolfballhasadiameterof1.68inches.Golfballs For usewiththelesson“SurfaceAreaandVolume ofSpheres” Practice 12 mm Thevolume ofasphereis972 continued Circumference of great circle 8 Ĭ in. Ĭ Surface areaof cubiccentimeters. What isthe

sphere 49 Ĭ ft 2 Ĭ

. Date ———————————— Volume ofsphere Super-Fly Super-Fly 288 Practice Workbook Ĭ m 3 Geometry XL

225 226

6. factor ofAtoB.Findthesurfaceareaandvolume ofSolidB. Solid A(shown)issimilartoB(notshown) withthegivenscale C. 5. scale factor. Tell whetherthepairofrightsolidsissimilar. Ifso,determinethe Name

3. 1. Practice Workbook Geometry LESSON 11.9 cl atro :2 of1: Scalefactor A. Multiple Choice to arightcylinder thatissimilartothecylinder shown? S ———————————————————————

r r 42 ft 10 mm

5 5 14 cm For usewiththelesson“ExploreSimilarSolids” Practice 10, 2, 2 A h , h

V 5

5 5 36 ft 19 Which set of dimensions corresponds Whichsetofdimensionscorresponds 6 cm 6 mm 8 cm 4 mm 3

7 cm D. 5 mm B. 7. cl atro :3 of1: Scalefactor S r r 3 cm 4 cm

5 5 96 m 15, 3, 4 mm 4 mm h h 5

5 2 A 7 ,

27 V 4. 2.

96 m 6 ft 3 m

3 ft 8. Date cl atro :3 of2: Scalefactor 4.5 m S

5 ———————————— 75.6cm 2 m 4 ft 1.8 m 2 ft 5 in. A 2 , V 9 in.

5 36 cm 36

2.7 m 1.2 m 3

Solid AissimilartoB.Findthescalefactorof 9. Name 13. 11. 10. LESSON 11.9

96 areaof16 has asurface Multiple Choice Finding Surface Area A. ——————————————————————— Ĭ S

} 4 1 =208m . What istheratioofvolumes ofthecylinders?

For usewiththelesson“ExploreSimilarSolids” Practice A 2 V V =64ft =27ft Two right cylinders aresimilar. areasare24 The surface B A 3 3 w pee aeasaefco f1:3. The smallersphere Two : spheres have of1 ascalefactor S Ĭ =52m squarefeet.Find areaofthelarger thesurface sphere. continued B. B

} 8 1

C. 2

14. 12.

S =63

} 2 1 V

=54in. B p cm A 2 3 Date S =28 ———————————— Ĭ and A p cm D. V

2 =16in. } 3 2 Practice Workbook

B 3 Geometry 227 228 Water Tower In Exercises18–22,usethefollowinginformation. Solid AissimilartoB.Findthesurfaceareaandvolumeof water tower. to12inchesof the actual 0.5 inchinyour modelwillcorrespond tower’s diameteris12feetandtheheight16feet. You decidethat of makingascalemodelthewater tower inyour town. The water Name 22. 21. 20. 19. 18. 17. 15. Practice Workbook Geometry LESSON 11.9 Useyour resultfromExercise 21toﬁndthevolume ofthemodel. Whatisthevolume oftheactualwater tower? areaofthemodel? Whatisthesurface Whatistheradiusandheightofmodel? Whatisthescalefactor? the larger cube? areaof areaofthesmallercube tothesurface What istheratioofsurface Finding aRatio ——————————————————————— 4 m A For usewiththelesson“ExploreSimilarSolids” Practice 2 As part ofaclassproject,you Aspart obtaintheresponsibility 4 m 3 m 4 m Two cubeshave volumes of64cubicfeetand216 cubicfeet. B continued 8 m

16.

Date 18 mm 12 mm 16 ft ———————————— 12 ft B

10 mm