Geometry Name: ________________________ Final Exam Benchmark Review Packet Period: _________

Chapter 2 Logic 1.

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10. Use deductive reasoning the draw a conclusion from the two given statements.

If a number is a multiple of 64, then it is a multiple of 8.

If a number is a multiple of 8, then it is a multiple of 2.

A. If a number is a multiple of 64, then it is a multiple of 2.

B. The number is a multiple of 2. C. The number is a multiple of 8. D. If a number is not a multiple of

2, then the number is not a multiple of 64.

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16. The Venn diagram shows Leilas graduating classes from middle school, high school, and college. How many students graduated together from both Leilas middle school and high school?

Chapter 4 Congruent Triangles 17. What is the definition of vertical angles? Draw an example of vertical angles with possible angle

measurements.

18. What are all of the types of angles that can be congruent to each other?

19. What other piece of information is needed to show UTV FGE by HL Congruence Theorem?

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27. What other piece of information is needed to show XYW BYW by SSS Congruence Postulate?

28. Identify the congruent triangles. How do you know they are congruent?

29. For each set of triangles, name the theorem or postulate that is a reason why the given triangles are congruent.

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30. Which theorem or postulate can not be used to prove two triangles are congruent? A. AAA B. SSA C. HL D. A and B E. None of the above

31. Two sides of a triangle have lengths 6 and 17. Which expression describes the possible lengths of the third side?

A. 6 17x< < B. 17 6x< < C. 23 11x< < D. 11 23x< <

32. Given three lengths of segments, how do you know it will create a triangle?

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33. What angles are congruent in these two triangles?

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Chapter 6 Similarity 35. Find the height of the tree.

36. Find the value of x.

37. A pole 2.4 feet tall cast a shadow of 1.3 feet. At the same time, a tree cast a shadow of 2.9 feet. How tall is the tree?

38. The two hexagons are similar. Find the scale factor from the larger hexagon to the smaller hexagon. Then find the value of x and y.

39. Determine if the triangles are similar. If so, state by which theorem, find the scale factor, and write the similarity statement.

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41. Theres a ladder that touches a wall 5 meters high, and the base of the ladder is 8 meters away from the wall. At the same time, theres a second ladder whose base is 28 meters away from the wall. How far up the wall does the second ladder touch?

42. Find the value of x.

Chapter 9 Transformations 43. Which type of transformation creates a similar

figure?

44. Which types of transformations create congruent figures?

45. Three transformations will be performed on triangle ABC. Which set of transformations will always produce a congruent triangle?

A. Dilation, rotation, translation B. Reflection, dilation, translation C. Rotation, translation, reflection D. Rotation, reflection, dilation

46. Which statement is true about dilations?

A. Dilations form similar images. B. Dilations are isometries. C. Dilations are the combination of two

reflections. D. Dilations form congruent triangles.

Chapter 10 Circles 47. Name the special segment or line using the circle given.

a. Radius b. Diameter c. Chord d. Tangent e. Secant

48. Find mPQR and mPR in the circle shown.

49. If the 113m X = and the 87m Y = , find the m Z and m W .

50. The NUK Energy Company is designing a new logo, as shown in the diagram, with 125mNK = and mNK mNU= .

What is the measure of KNU ?

51. What is the area of the red portion on the spinner if the radius is 5 cm?

Find the value of x.

53. What is the distance around the edge of the clock from the 11 to the 4 when the radius is 5 inches?

54. Find m PSQ if 6 5m PSQ y = and 2 15m PRQ y = + .

55. Find the value of x.

56. Find AO when AB is tangent to circle O.

57. Solve for the value of x.

Chapter 11 Area and Perimeter 58. Find the area of the figure shown.

59. Find the area of the shaded region if the polygon is a regular hexagon.

60. What is the area of one sector of this dart board? The radius is 8 inches and each section is evenly spaced out.

61. What is the probability that something will land on the inside square given the outer edge of the square is 7 cm?

62. If the length of a rectangle is tripled, what will happen to its area?

63. If the length of a square is doubled, what will happen to its area?

64. What is the area of the shaded region?

65. What is the probability of something landing in the white area?

66. Find the area of the regular hexagon.

67. Find the area of the regular hexagon given the side length is 3.728 centimeters.

68. Find the perimeter and area of the shape shown.

69. What is the definition of a midsegment in a figure? What does it connect together?

Chapter 12 Surface Area and Volume 70. A classroom globe has a diameter of 18 inches.

What is the volume of the globe?

71. What is the surface area of the pyramid?

72. A right cylindrical can is 10 inches high and the length of its radius is 6 inches. What is the minimum number of square inches of construction paper needed to cover the lateral surface of this can?

73. The right pyramid below has a square base measuring 14 centimeters on each side, and a slant height of 10 centimeters. What is the difference between the total surface area and the lateral surface area of the pyramid?

74. What is the volume of this can?

75. How many faces, edges, and vertices does the shape below have? Is the polyhedron concave or convex?

76. The figure shown is a cylindrical solid with a circular cylindrical hole drilled out of the center. Find the surface area of the resulting solid.

77. Find the surface area of the right cone shown.

78. Find the volume and surface area of the cylinder below.

79. The pyramid shown has a rectangular base and faces that are isoseles triangles. Find its volume.

80. To the nearest cubic foot, the cylindrical natural gas storage tank shown holds 2453 cubic feet of gas. To the nearest cubic foot, what is the approximate volume of an equally tall tank if it has a diamter of 31.25 feet?

81. Calculate the volume of the cone.

82. The machinist drilled a conical hole into a cube of metal. The edges of the cube are 12 cm. What is the volume of the metal after the hole has been drilled?

83. A childrens tent is a pyramid with a square 6-by 6 foot base. The tent has a volume of 72 cubic feet. A larger model of the tent is also available. It has the same height, but its square base is 9 feet wide. What is the cubic feet of space inside the larger tent?

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95. Find the total volume of the solid.

96. Find the total surface area of the solid.

97. How many faces, vertices, and edges does this solid have?

98. Solid A (shown) is similar to Solid B (not shown) with the given scale factor of A to B. Find the surface area and volume of Solid B.

99. Find the scale factor of solid A to solid B. Write as a decimal and round to the nearest tenth.

100. Sally has a sandbox for her daughter that she wants to decrease in size. She wants each edge of the sandbox to be decreased by half of its original length. How does the volume of the new sandbox compare to the volume of the original sandbox by percentage?