Diamond in the Rough the Pythagorean Theorem

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B © 2010 College Board. All rights reserved. _ M S 3 _ 6 - 1 Diamond intheRough The PythagoreanTheorem _ regulation diamond. baseball might helpful be for determining if Cameron can throw across a lengths the between of of three sides the any right triangle that diamondbaseball into two right triangles. " diamondbaseball and feet is 90 baselines are the perpendicular. hesecond if is able to throw feet? 130 the baseball to. Will able he be to consistently throw to out steal trying runners b. a. 1. regulation a is size to steal second However, base. trying diamond school the baseball from ball the home plate to second to base throw out runner a has played thecommunity in baseball and is able to easily throw Cameron catcher a is out trying for team. baseball He school the Activating Knowledge, Prior Visualization, Interactive Word Wall Reading, Shared STRATEGIES: LEARNING SUGGESTED S E e imaginary line from e imaginary home plate divides to second base the . i n d of right the below. triangle Use terms the " d

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3 0 of right a triangle. Explain di the 3 hypotenuse ! eld andeld larger than the 3rd # erences hypotenuse the between and legs the 90 ft 90 ft and Pitcher Home 2nd leg to and identify parts label the 90 ft 90 ft " ! ere relationship a is eld he is accustomed 1st Unit 6• Three-Dimensional Geometry related ratesproblems. theorem isusefulwhensolving In APCalculus,thePythagorean CONNECT TO My Notes AAP P ACTIVITY 6.1 112/30/09 12:06:49 PM 303 2 / 3 0 / 0 9

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P M 3303-310_SB_MS3_6-1_SE.indd 304 0 3 - 3 1 0 _ S 304 B continued ACTIVITY _ M The MATH TERMS the legs of the triangle. of the squares of the lengths of right triangle is equal to the sum length of the hypotenuse of a states that: S 3 _ 6 - SpringBoard Pythagorean theorem 1 _ S E . i n d d 6.1

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3 0 My Notes 4 ® The PythagoreanTheorem DDiamond intheRough Mathematics withMeaning i a m

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R a In right a triangle, let leg in eachof in leg following the triangles. Use Pythagorean the theorem to hypotenuse eachof in following the triangles. Use Pythagorean the theorem to o Pythagorean theorem Pythagorean and TM u Level3 Text, Create Representations, Think/Pair/Share, Group Group Work Presentation, Backwards Think/Pair/Share, Representations, Create the Text, Questioning STRATEGIES: LEARNING SUGGESTED Pythagorean theorem. Write an equation using Draw and label right a triangle using 3 7 g h b be the lengths the of be of legs the triangle. the 4 c b 25

c be the length the of be hypotenuse the and let describes triangles containing describes right a a , b and " " nd the lengthnd the of missing the lengthnd the of the b. b.

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B © 2010 College Board. All rights reserved. _ M S 3 _ 6 - 1 _ 9. calculator, estimation o is it mayBecause di be 8. 7. 6. 5. Think/Pair/Share,Representations, Group Group Presentation, Discussion Create STRATEGIES: LEARNING SUGGESTED The PythagoreanTheorem DDiamond intheRough S E . i i n a d baseball diamondbaseball showing the Sketch diagram a of regulation a Use Pythagorean the theorem to estimated length of hypotenuse. the below. hypotenuse for table the in eachof right the triangles described Use Pythagorean the theorem to without calculator? a Why or why not? distanceCan the from home plate found to be second base home plate to second base. Write an equation that to used can be triangles? are lengths the of legsof the the and of legs any right What triangles. Identify and hypotenuse label the from home plate to second base. line andbaselines imaginary the d m

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cult to R o u # en a useful problemen a useful solving tool. g p Length of h ! Leg 2 nd some distances without a r t ! ! nd nd the exact length of exact nd the the of Hypotenuse of Exact Length p ! nd distance the from interms of r and ! nd the Estimated Length of Hypotenuse of t . Unit 6• Three-Dimensional Geometry calculator. using technologysuchasa irrational numbersarefound Decimal approximationsof written usingaradicalsign. an irrationalnumbermustbe number. Theexactvalueof and iscalledanirrational does notterminateorrepeat is adecimalnumberthat perfect square,theresult of anumberthatisnot If youtakethesquareroot My Notes TECHNOLOGY ACTIVITY continued

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3 0 My Notes 6 ® The PythagoreanTheorem DDiamond intheRough Mathematics withMeaning i a m o n d

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R to consistently throw to base? steal second out trying arunner If Cameron can throw able he be will feet, 130 the baseball Showbase. your all work. table inItem 9to Use Pythagorean the theorem and information the inthe Justifyto base? second your choice. help Cameron estimate distance the from home plate Which of table triangles the in the Item in to couldused 9 be consecutive feet 60 is and are bases baselines the perpendicular. regulation a On so Explain your reasoning. o TM u Level3 Activating Prior Knowledge Prior Activating Presentation, Group Think/Pair/Share, Problem, the Simplify STRATEGIES: LEARNING SUGGESTED ! distancethe from home plate to on second base a so Use Pythagorean the theorem and your sketch to estimate Sketch and drawing label scale a of so a g eld. Show your all work. h ! nd distance the from home plate to second " ball diamond,ball thedistance between " ball diamond.ball " ball 112/30/09 12:07:03 PM 2 / 3 0 / 0 9

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B © 2010 College Board. All rights reserved. _ M S 3 _ 6 - 1 _ 16. 15. 14. bat will box at an angle as shown in the diagram below. He wonders if the might still be able to use the box. His idea is to put the bat in the having abox long enough for 34˝bat. the Cameron he thinks box to be 16˝ long mightbe enough.A the bat home. he speak to the concierge at the hotel about options for shipping autographed bat he won home on the plane. His dad suggests that of vacation, he discovers that he will not be able to carry the his favorite baseball team, the Anglers, play. On their last day During summer vacation, Cameron’s parents take him to see Visualization, Representations, Think/Pair/Share Create Reading, Subtask a Identify Shared STRATEGIES: LEARNING SUGGESTED The PythagoreanTheorem DDiamond intheRough S E . i i n a d necessary calculations. necessary Find length the of diagonal the of box. the Show any Show any work to needed What are lengths the of of legs the right triangle? this diagram the triangle in above.Outline this ! d m

e diagonal e of box the hypotenuse the is of right a triangle.

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R 27˝, the concierge 27˝,the apologizes for not o " u er measuring the dimensions of the g 27 in. h # nd these lengths.nd these 16 in. 16 in. Unit 6• Three-Dimensional Geometry reservations totravelplans. tasks rangingfromrestaurant who helpsguestswithvarious In ahotel,conciergeisperson CONNECT TO My Notes TTRAVEL R A ACTIVITY V E L continued 112/30/09 12:07:07 PM 307 2 / 3 6.1 0 / 0 9

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3 0 My Notes 8 ® The PythagoreanTheorem DDiamond intheRough Mathematics withMeaning i a m o n d

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R why Pythagorean the She excited is and some do will investigation tells they him into how he applied Pythagorean the When Cameron returns to school, he tells his math teacher your response. Will Cameron able be box the to to use ship bat? his Justify o TM u Level3 Group Presentation, Create Representations Create Presentation, Group Think/Pair/Share, STRATEGIES: LEARNING SUGGESTED Triangle 2: 5 units 5 and units 12 units 3 and units 4 Triangle 2: Triangle 1: Use one piece of paper for eachtriangle. triangles having with legs eachof following the lengths. centimeterOn paper or grid graph paper, draw right of triangle? the How area the does of each square relate to length the of a leg of each of squares these and complete table the below. same of the leg sides length the as triangle. the Find area the of eachleg On eachof right the draw triangles, square a with Hypotenuse of Triangle 3: Hypotenuse of Triangle 2: Hypotenuse of Triangle 1: hypotenuse eachof in triangles. the Use Pythagorean the units 8 and units 15 Triangle 3: g h Length of Leg 1 Area of Square ! on Leg 1 Leg on eorem works. ! eorem to ! eorem on while vacation. Length of " nd the lengthnd the of the Leg 2 Area of Square on Leg 2 Leg on 112/30/09 12:07:10 PM 2 / 3 0 / 0 9

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B © 2010 College Board. All rights reserved. _ M S 3 _ 6 - 1 _ i. h. g. f. e. Representations Create Presentation, Group STRATEGIES: LEARNING SUGGESTED The PythagoreanTheorem DDiamond intheRough S E . i i n a d d m

3 0 ! How relationship this does illustrate Pythagorean the built on hypotenuse? the Explain your reasoning. drawn on each of of legs the triangle and the large the square What relationship the is areas the between of squares the Area of square on hypotenuse the of Triangle 3: Area of square on hypotenuse the of Triangle 2: Area of square on hypotenuse the of Triangle 1: each triangle. Find area the of square the created on hypotenuse the of equal to of length the hypotenuse the of triangle. the to createnecessary one larger square having length side You may cut and rearrange squares small the any way to build large a square on hypotenuse the of that triangle. Use the small squares drawn on the legs of each right triangle of legs. the Cut out each of trianglesand the squares the drawn on each o 9 eorem form the in n d

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2 ? Unit 6• Three-Dimensional Geometry My Notes ACTIVITY continued 112/30/09 12:07:14 PM 309 2 / 3 6.1 0 / 0 9

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R nearest tenth of a unit. Find distance the from point (3, 1) to point (5, 5) to the nearest tenth of a unit. Find distance the from point (1, 2) to point (7, 6) to the o TM u Level3 g ! h endraw legsand the " nd the distancend the 7. 6. 5. 4. point (8, 3) to nearest the tenth of a unit. Find distance the from point (2, 6) to d. c. b. a. following: Estimate square the roots of of each the ladder? is 15 feet from house. the How long is the above ground. the ! windowstory on house the she is painting. painterA to ladder a reach uses second- a type of is type triangle your answers. REFLECTION MATHEMATICAL e bottom of window the is 20 feet 40 12 17 99 y

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