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Home , Isosceles trapezoid, Kite (geometry), Rhomboid

Created by: Jasmine E. Aue MATH 205 [email protected] This form is a review sheet for MATH 090 students based primarily around the teaching & instructions of Professor V. Smith of ESU.

HELPFUL TIPS FOR COURSE CONTENT (​ie. not formulas but important​) FORMULA LIST ℉ = ((℃/5)(9)) + 32 | Lines, Arrows, Points & Planes Fahrenheit to Celsius formula This section is a review of lines, arrows, points & planes. How they are defined, look and interact with each other. ℃ = ((℉ − 32)/9)(5) ​ |​ Celsius to ❏ Collinear​: same Fahrenheit formula ❏ 2 Coplanar​: same plane a2 + b = c2 |​ Pythagorean ❏ ● ● Closed​: a line with an endpoint on each end, kind of like this Theorem ❏ Half​: a line with only one endpoint, kind of like this ● d = (x − x ) + (y − y ) ❏ Open​: a line with no endpoints, like this √ 2 1 2 1 | ❏ → ⋃ → = ↔ of a ❏ → ⋂ → = r2 = (x − h)2 + (y − k)2 |​ ❏ ●● ⋃ ●→ = → Formula ❏ FE￮ ⋂ ￮ ￮ ￮ → → = a2 + b2 = c2 |​ Pythagorean ❏ Intersecting Lines​: lines that have only one in common ❏ Intersecting Planes​: planes that have only one line in common Theorem ❏ Skew​: cannot be coplanar y = mx + b ​ |​ y is from (x,y), m ❏ Concurrent​: 3 or more intersections at the same point is the slope, x is from (x,y) & b ❏ Parallel​: same slope, non-intersecting is the y-intercept

m = (y2 − y1) / (x2 − x1) |​ this is ❏ There is exactly one line containing any two distinct points the point-slope formula, use ❏ If two points are in a plane then the line of points are in a plane this to find the slope of a line ❏ If two planes intersect, there is a line at that intersection given two coordinate pairs ❏ There is exactly one plane that contains any 3 distinct (x1, y1) & (x2, y2) noncollinear points P = 4s ​ |​ of a ❏ Collinear points/lines can have infinitely many planes 2 ❏ One line + one point = a unique line A = s ​ |​ of a Square ❏ Parallel lines are on one plane P = 2w + 2l ​ |​ Perimeter of a ❏ Two intersecting lines are on one plane

A = lw ​ |​ Area of a rectangle

C = πd = 2πr ​ |​ of a Circle

A = πr2 ​ |​

P = a + b + c ​ |​ Perimeter of a

A = 1 bh ​ |​ Area of a Triangle ABAY 2

Angles & A = bh ​ |​ Area of a This section is a review of and circles, not including their formulas (​see formula list for formulas​). ❏ Complementary Angles: add to 90° 1 A = 2 (b1 + b2)h ​ |​ Area of a ❏ Supplementary Angles: add to 180° ❏ Acute Angles: less than 90° A = 1 d d ​ |​ Area of a Diamond ❏ Right Angles: equal to 90° 2 1 2 ❏ Obtuse Angles: greater than 90° but less than 180° SA = 2B + P h ​ |​ Surface Area of ❏ Reflex Angles: greater than 180° but less than 360° a Right Prism, where B = area ❏ Straight Angles: equal to 180° of the base and P =perimeter ❏ Circle: 360° of the base ❏ 1 360 = 1° = 60′ = 3600" (when going from degrees to minutes to V = Bh ​ |​ Volume of a Right seconds, multiply & when going from seconds to minutes to Prism degrees, divide) SA = 2lh + 2wh + 2lw ​ |​ Surface Diagrams Related to Angles and Circles: l Area of a Rectangular Prism V = lwh ​ |​ Volume of a Rectangular Prism

2 SA = 6s ​ |​ Surface Area of a me Cube

V = s3 ​ |​ Volume of a Cube

SA = 2πrh + 2πr2 ​ |​ Surface Area

of a Right Cylinder (regular cylinder like a pringles can) N V = πr2h ​ |​ Volume of a Right Cylinder

2 SA = 4πr ​ |​Surface Area of a Interior Angles: 3, 4, 5, 6 Sphere

Exterior Angles: 1, 2, 7, 8 4 2 V = 3 πr ​ |​ Volume of a Sphere Alternate Interior Angles: 3 & 6, 4 & 5 SA = B + 1 P l ​ |​ Surface Area of Alternate Exterior Angles: 1 & 8, 2 & 7 2 Corresponding Angles: 1 & 5, 2 & 6, 3 & 7, 4 & 8 a Pyramid (using slant height) lwh V = 3 ​ |​Volume of a Pyramid WHN Arc Minor 2 SA = πr√r2 + h + πr2 ​ |​ Surface I the transversal 2 2 l is Chord Area of a Cone where √r + h is the slant height

\ 1 2 V = 3 πr h ​ |​ Volume of a Cone r

Center

Arc Major K(O,r) Radius d = a + b Circle “name” Normal Distribution This is a diagram of Normal Distribution:

STUDY TIPS

Scheduling |​ keep up to date with all assignments, quizzes, tests, exams, etc. by

documenting them onto a calendar you regularly check, using a reminders app, a planner or other scheduling

tool(s)

Review |​ attend regular tutoring sessions, create your own mock tests using practice Shapes problems, review past HW, quizzes, tests & exams This section is a review of shapes, will have their own more detailed section following this one. (​see formula list for formulas on area, perimeter, volume, etc.​) Eat Well |​maintain a healthy, ❏ Simple​: does NOT intersect itself balanced diet to increase ❏ Closed​: the start of the shape is also its end & vice versa. brain function (memory, ❏ Regular ​: equilateral (sides) & equiangular (angles) engagement, attention, etc.) ❏ Trapezoid​: at least one pair of parallel lines & to decrease fatigue, ❏ ​: 2 pairs of adjacent & congruent angles fogginess, etc. ❏ Parallelogram​: Both pairs of opposite sides are parallel ❏ ​: two adjacent sides are congruent Sleep Well |​ maintain a health sleep schedule of 6-8 hours of Diagrams Related to Shapes: sleep per night

TUTORING INFORMATION

.. ... ESU Tutoring Website |

https://www.esu.edu/tutoring g. /index.cfm ESU’s WCOnline Tutoring

Link | https://esu.mywconline.com

" - " / i I wearE T

Ex . every quay is a rectangle . every trapezoid is a .

NOT is a . EX . every rectangle quay

Not every is a rectangle . Triangles This section is a review of Triangles. (​see formula list for formulas for area, perimeter, etc.​) Diagrams Related to Triangles:

Special Triangles

Miscellaneous Information This section is a review of miscellaneous information that does not fit a big enough category to be a separate section. These concepts are just as important though! ❏ Area is always squared (x2) ❏ Volume is always cubed (x3) π ❏ When going from x° to radians; x° • 180° 180° ❏ When going from radians to x° ; x • π ❏ Kilo (1000), Hecto (100), Deka (10), GRAM (Base Measurement, 1),Deci (0.1), Centi (0.01), Milli (0.001) ❏ 1 Ton = 1000000g = 1000kg ❏ 1kg = 1000g ❏ 1hg = 100g ❏ 1dkg = 10g ❏ 10dg = 1g ❏ 100cg = 1g ❏ 1000mg = 1g ❏ 1cm3 = 1mL = 1g ❏ 1dm3 = 1L = 1kg ❏ 1yd2 = 36in2 ❏ 1ft = 12in ❏ 1yd = 3ft = 36in ❏ 1mi = 1760yd = 5280ft = 63360in

Vectors:

iBBq

Name______

GEOMETRY FINAL EXAM REVIEW

I. MATCHING _____reflexive A. a(b + c) = ab + ac _____transitive B. If a = b & b = c, then a = c. _____symmetric C. If D lies between A and B, then AD + DB = AB. _____substitution D. If a = b, then b = a. _____distributive E. a = a

_____definition of midpoint F. If D is the midpoint of ̅̅̅ ̅, then AD = AB.

_____midpoint theorem G. If a + b = c and a = d, then d + b = c.

_____segment addition postulate H. If D is the midpoint of ̅̅̅ ̅, then AD = DB.

II. Fill in the blank. 1. An is also a(n) ______triangle. 2. The ______is the longest side of a . 3. Similar triangles have congruent corresponding ______and the corresponding ______are in proportion. 4. In an , the ______angle is the that is different. 5. The ______of a triangle is a segment from a to the midpoint of the opposite side. 6. A(n) ______of a triangle is a segment from a vertex to the opposite side. 7. A(n) ______of a segment is a line, segment, or ray to a segment at its midpoint. 8. The measure of a central angle is ______to its intercepted arc. 9. Two ______angles have a sum of 90. 10. Two ______angles have a sum of 180. 11. A ______has only 1 endpoint. 12. If two lines are ______, they form right angles. 13. Two lines intersect in a ______. 14. Two planes intersect in a ______. 15. Through any three collinear points there are ______. Through any three non-collinear points there is ______. 16. ______angles measure between 0 and 90. 17. ______angles measure between 90 and 180. 18. Find the side of square with area 16 units2. ______. 19. If the ratio of the measures of the angles of a triangle is 2:2:5, then the triangle is a(n) ______triangle. 20. If 4 points all lie on the same line, then the points are ______. 21. The interior angle sum of a is ______. 22. The exterior angle sum of a is ______. 23. If each interior angle of a is 144, then the polygon is a ______. 24. If each exterior angle of a regular polygon is 30, then the polygon has ______sides. 25. In a 30 - 60 - 90 triangle, the long leg is ______times the short leg. 26. In a 45 - 45 - 90 triangle, the hypotenuse is ______times the leg. 27. An angle inscribed in a semicircle is a ______angle. 28. Write 32 in simplest radical form. ______29. If A is a right angle and m A = (4x + 10)°, then x = ______.

1 2 a 3 4

a b 5 6 b 7 8

30. 3 & 5 are ______angles & therefore are ______. 31. 4 & 5 are ______angles & therefore are ______. 32. 2 & 6 are ______angles & therefore are ______. 33. If m 6 = (x + 5)° and m 4 = (2x + 10)°, then m 4 =______.

34. True or False. A triangle may have sides of 7, 12, and 18. 35. To find the area of a right triangle, the ______can be used as the base and height.

36. ̅̅̅ ̅ is a ______. D 37. ̅̅̅ ̅ is a ______. 38. ̅̅̅ ̅ is a ______. 39. ⃡ is a ______. A B 40. ⃡ is a ______. O 41. Point O is the ______. 42. Point A is the ______. C

43. x = _____ D 44. m ABD = _____ E

(3x + 10)° (4x)° (4x – 50)° A B C 45. x = _____

9 x 8 4 4

A 46. B and E are the midpoints of AD and AG. If DG = 40, then CF _____.

B E

C F

D G

47. Find the perimeter of a right triangle with legs 6 and 8. _____ 48. If the of a rhombus are 20 and 36, then the area is _____. 49. Find the area of a right triangle whose hypotenuse is 25 and whose leg is 7. _____

Name the theorem or postulate used to prove the triangles congruent. 50. ______51. ______

52. ______53. ______

C

54. m = _____

55. m =_____ 56. m COB = _____ 57. m AOB = _____ A O E B 58. Draw ACB. m ACB = ______

Given: O is the center.

m = 130 D Z XYZ is an equilateral triangle. 59. ZY = _____ 60. m Z = _____ 61. altitude = _____

X 8ft Y

62. Area of Circle = _____ 63. Area of Square = _____ 64. Area of shaded region = _____ 5 65. Circumference of Circle = _____ 66. Perimeter of Square = _____

67. Area of parallelogram = _____ 12

60 20

Round your answer to the nearest whole number or degree. y 68. Find x ______.

69. Find y ______6.1 37

35 x° 4

70. A ladder is positioned against a house at a 65 angle. The ladder is 10 feet tall. How far away from the house is the base of the ladder? Round your answer to the nearest tenth.

71. x = _____ 72. y = _____ x y 73. z = _____ z

105

120

74. x = _____ x 4

6

8

75. 2 lines drawn to a circle from the same point are ______. 76. If the diagonals of a quadrilateral are , then the quad. is a ______or a ______. 77. If the diagonals of a quad. are and , then the quad. is a ______. 78. If the diagonals of a quad. are , then the quad. is a ______or a ______. 79. The legs of an are 10 ft. and the bases are 10 ft. and 22 ft. The length of the median is _____. The area of the trapezoid is ______. 80. In a parallelogram, ______angles are supplementary and ______angles are congruent. _____ 81. Given ∆XYZ ∆RSN, then Y _____ and XZ _____.

82. x = _____ x

150 80

_____ O is the center & WX is tangent to Circle O.

W 83. m = 100, m = 90, m X = _____

84. is a ______arc. O X Y Z 85. is a ______arc.

86. Find the volume of a rectangular prism with length 6 in, width 3 in, and height 4 in. 87. Find the total (surface) area of a cylinder with radius 4 m and height of 3 m. 88. The total (surface) area of a cylinder is 66π cm2 and the radius is 3 cm. Find the volume. 89. What is the volume of a cone whose radius is 9 and slant height is 13? 90. The total (surface) area of a sphere is 64 . Find the radius of the sphere.

B D

91. Find m BCD.

70 80 A C E

______92. Given: Y is the midpoint of XZ and WV . V Prove: W V X Y

W Z

B

93. List the sides from largest to smallest. 70°

80° A C

94. Points A, B, and C are collinear. If AC = 8, BC = 6, and AB = 14, which point is in between the other two? ______

95. OA = 8 and m AOB = 90. Find AB.

O A

B 96. In O, the radius is 41, and XZ = 18, find OM. X

Y O M

Z

97. Find the scale factor of two if the are 36 cm and 48 cm respectively.

98. Name the transformation.

99. Name the transformation that maps A ABC to ADE.

D E

B C

100. Two similar are shown. Find the scale factor and the value of x.

101. YZ = √ and XZ = √ . Find XY. Answer in simplified radical form. Y

X Z

102. Describe the triangle with sides of 8, 2√ , 9.

103. If the hypotenuse in an isosceles right triangle measures 6√ ft., then the length of each leg is ______.

104. Find the volume of a square pyramid with base 5 in. and height 3 in.

Answers 36) Radius 79) 15 ft. and 128 ft2 Matching 37) Diameter 80) Consecutive; E, B, D, G, A, H, F, C 38) Chord Opposite Fill in the Blank 39) Secant 81) S; ̅̅̅ ̅ 1) Equiangular 40) Tangent 82) 70° 2) Hypotenuse 41) Center 83) 35° 3) Angles; sides 42) Point of Tangency 84) Minor 4) Vertex 43) 20 85) Major 5) Median 44) 70° 86) 72 units3 6) Altitude 45) 6 87) 56π units2 7) Bisector 46) 30 88) 72π cm3 8) Equal 47) 24 units 89) 54π√ units3 9) Complementary 48) 360 units2 90) 4 10) Supplementary 49) 84 units2 91) 75° 11) Ray 50) SAS 92) Y is the midpoint 12) 51) ASA of ̅̅̅ ̅ and ̅̅̅̅ ̅ 13) Point 52) HL or AAS (Given), ̅̅̅ ̅ 14) Line 53) SSS ̅̅̅ ̅ ̅̅̅̅ ̅ ̅̅̅ ̅ 15) Infinite Planes; 54) 50° (Def of Midpoint), Exactly One Plane 55) 50° 16) Acute 56) 50° (Vertical Angles 17) Obtuse 57) 180° are Congruent),

18) 4 units 58) 90° (SAS), 19) Isosceles 59) 8 (CPCTC) 20) Collinear 60) 60° 93) ̅̅̅ ̅ ̅̅̅ ̅ ̅̅̅ ̅ 21) 720° 61) √ 94) C 22) 360° 62) 25π units2 95) 8√ 23) Decagon 63) 100 units2 2 96) 40 24) 12 64) (100 – 25π) units 97) 25) √ 65) 10π units 26) √ 66) 40 units 98) Reflection 27) Right 67) √ units2 99) Dilation

28) √ 68) 57° 100) and x =

29) 20 69) 28 101) √ 30) Same Side Int.; 70) 4.2 ft. 102) Obtuse Supplementary 71) 75° 103) 6 ft. 31) Alt Int; 3 72) 75° 104) 25 in Congruent 73) 30° 32) Corresponding; 74) 3 Congruent 75) Congruent If you would like detailed answers 33) 120° 76) Rhombus; square please visit an MQC tutor (Tutoring 34) True 77) Square Department contact information on 35) Legs 78) Rectangle; Square pg. 3)