Name: ________________________ Class: ___________________ Date: __________ ID: A

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2nd Semester Exam Review - Geometry CP

1. Complete this statement: A polygon with all sides the same length is said to be ____.a. regularb. equilateralc. equiangulard. convex

2. WXYZ is a parallelogram. Name an angle congruent to ∠WXY.

a. ∠WZXb. ∠WZYc. ∠YZXd. ∠XYZ

3. Which statement can you use to conclude that quadrilateral XYZW is a parallelogram?

a. WZ ≅ XY andXW ≅ WZ

b. WZ ≅ ZY andXW ≅ YZ

c. WZ ≅ XY andXW ≅ YZ

d. WN ≅ NZ andYN ≅ NX

4. Classify the figure in as many ways as possible.

a. rectangle, square, quadrilateral, parallelogram, rhombus

b. rectangle, square, parallelogramc. rhombus, quadrilateral, squared. square, rectangle, quadrilateral

5. The two rectangles are similar. Which is the correct proportion for corresponding sides?

a.12

8=

24

4b.

12

4=

24

8c.

12

4=

8

24d.

4

12=

24

8

Name: ________________________ ID: A

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Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale.

6.

a. 13.27b. 17.55c. 10.58d. 176

7.

8. AB = 15, BC = 9, and CD = 10

Name: ________________________ ID: A

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Determine whether each pair of triangles is similar. Justify your answer.

9.

Find x and the measures of the indicated parts.

10. AB

11. AB12.

If m∠BDC = 35, m arcAB = 100, and m arcCD = 100, find m∠1.

Name: ________________________ ID: A

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13.

If m∠1 = 2x + 2, m∠2 = 9x, find m∠1.

14. Find x. Assume that segments that appear tangent are tangent.

15. Find x. Assume that segments that appear tangent are tangent.

Find x. Assume that any segment that appears to be tangent is tangent.

16.

17.

Name: ________________________ ID: A

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Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent.

18.

19. Find the values of the variables in the parallelogram. The diagram is not to scale.

20. In the parallelogram, m∠QRP = 57 and m∠PRS = 62. Find m∠PQR. The diagram is not to scale.

21. For the parallelogram, if m∠2 = 5x − 30 and m∠4 = 3x − 10, find m∠3. The diagram is not to scale.

22. LMNO is a parallelogram. If NM = x + 14 and OL = 2x + 7, find the value of x and then find NM and OL.

23. Find values of x and y for which ABCD must be a parallelogram. The diagram is not to scale.

Name: ________________________ ID: A

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24. In the rhombus, m∠1 = 3x, m∠2 = x + y, andm∠3 = 3z. Find the value of each variable. The diagram is not to scale.

25. Find the measure of the numbered angles in the rhombus. The diagram is not to scale.

26. In rectangle KLMN, KM = 5x + 16 and LN = 58.5. Find the value of x.

27. In quadrilateral ABCD, AE = x + 14 and BE = 3x − 18. For what value of x is ABCD a rectangle?

28. Find the values of a and b.The diagram is not to scale.

29. ∠J and∠M are base angles of isosceles trapezoid JKLM. If m∠J = 15x + 6, and m∠M = 14x + 14, find m∠K.

30. LM is the midsegment of ABCD. AB = 85 andDC = 119. What is LM?

Name: ________________________ ID: A

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31. LM is the midsegment of ABCD. AB = x + 8, LM = 4x + 3, andDC = 173. What is the value of x?

What is the solution of each proportion?

32. 3

a=

15

4033.

3y − 8

12=

y

5

Are the polygons similar? If they are, write a similarity statement and give the scale factor.

34.

Name: ________________________ ID: A

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The polygons are similar, but not necessarily drawn to scale. Find the value of x.

35.

36. Are the triangles similar? How do you know?

State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used.

37. 38. Use the information in the diagram to determine the height of the tree to the nearest foot.

Name: ________________________ ID: A

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39. Michele wanted to measure the height of her school’s flagpole. She placed a mirror on the ground 48 feet from the flagpole, then walked backwards until she was able to see the top of the pole in the mirror. Her eyes were 5 feet above the ground and she was 12 feet from the mirror. Using similar triangles, find the height of the flagpole to the nearest tenth of a foot.

40. Campsites F and G are on opposite sides of a lake. A survey crew made the measurements shown on the diagram. What is the distance between the two campsites? The diagram is not to scale.

41. What is the value of x, given that PQ Ä BC?

Find the length of the missing side. The triangle is not drawn to scale.

42. 43. Triangle ABC has side lengths 12, 35, and 37. Do the side lengths form a Pythagorean triple? Explain.

Name: ________________________ ID: A

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Find the length of the missing side. Leave your answer in simplest radical form.

44.

45. A triangle has side lengths of 38 in, 22 in, and 39 in. Classify it as acute, obtuse, or right.

46. In triangle ABC, ∠A is a right angle and m∠B = 45°. Find BC. If your answer is not an integer, leave it in simplest radical form.

47. Find the length of the leg. If your answer is not an integer, leave it in simplest radical form.

48. The area of a square garden is 128 m2. How long is the diagonal?

Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.

49.

50.

51. Find the missing value to the nearest hundredth.

52. Write the ratios for sin A and cos A.

Name: ________________________ ID: A

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Use a trigonometric ratio to find the value of x. Round your answer to the nearest tenth.

53. 54.

Find the value of x. Round to the nearest tenth.

55.

56.

57.

58.

59. Find the value of w, then x. Round lengths of segments to the nearest tenth.

Name: ________________________ ID: A

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Find the value of x. Round to the nearest degree.

60. 61.

Find the value of x to the nearest degree.

62.

63.

What is the description of ∠1 as it relates to the situation shown?

64. A spotlight is mounted on a wall 7.4 feet above a security desk in an office building. It is used to light an entrance door 9.3 feet from the desk. To the nearest degree, what is the angle of depression from the spotlight to the entrance door?

Name: ________________________ ID: A

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Find the area. The figure is not drawn to scale.

65. 66.

Find the area of the trapezoid. Leave your answer in simplest radical form.

67.

The figures are similar. Give the ratio of the perimeters and the ratio of the areas of the first figure to the second. The figures are not drawn to scale.

68. 69. The trapezoids are similar. The area of the smaller

trapezoid is 131 m2. Find the area of the larger trapezoid to the nearest whole number.

70. Find the similarity ratio and the ratio of perimeters

for two regular pentagons with areas of 25 cm2

and 64 cm2.

Name: ________________________ ID: A

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Find the circumference. Leave your answer in terms of π .

71.

Find the area of the circle. Leave your answer in terms of π .

72.

Find the surface area of the cylinder in terms of π .

73.

Name: ________________________ ID: A

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Find the volume of the given prism. Round to the nearest tenth if necessary.

74.

Find the volume of the cylinder in terms of π .

75.

76. Find the volume of the composite space figure to the nearest whole number.

Find the volume of the square pyramid shown. Round to the nearest tenth if necessary.

77.

Name: ________________________ ID: A

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Find the volume of the cone shown as a decimal rounded to the nearest tenth.

78.

Find the volume of the sphere shown. Give each answer rounded to the nearest cubic unit.

79.

Are the two figures similar? If so, give the similarity ratio of the smaller figure to the larger figure.

80.

81. Find the similarity ratio of a prism with the surface

area of 81 m2 to a similar prism with the surface

area of 196 m2.

82. Find the similarity ratio of a cube with volume 216

ft3 to a cube with volume 2744 ft3.

83. The volumes of two similar solids are 729 m3 and

125 m3. The surface area of the larger solid is

324 m3. What is the surface area of the smaller solid?

Name: ________________________ ID: A

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Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x. (Figures are not drawn to scale.)

84. m∠O = 145

85. m∠P = 23

86. AB is tangent to circle O at B. Find the length of the radius r for AB = 7 and AO = 8.6. Round to the nearest tenth if necessary. The diagram is not to scale.

87. JK , KL, and LJ are all tangent to O (not drawn to scale). JA = 13, AL = 9, and CK = 11. Find the perimeter of ∆JKL.

88. NA ≅ PA, MO ⊥ NA, RO ⊥ PA, MO = 7 ftWhat is PO?

Name: ________________________ ID: A

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Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale.

89.

90.

91. Find the measure of ∠BAC. (The figure is not drawn to scale.)

92. Find x. (The figure is not drawn to scale.)

93. Find m∠BAC. (The figure is not drawn to scale.)

Name: ________________________ ID: A

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94. m∠R = 42. Find m∠O. (The figure is not drawn to scale.)

95. If mBY = 40, what is m∠YAC? (The figure is not drawn to scale.)

96. mDE = 106 and mBC = 70. Find m∠A. (The figure is not drawn to scale.)

Name: ________________________ ID: A

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97. Find the value of x for mAB = 31 and mCD = 27. (The figure is not drawn to scale.)

98. Find m∠D for m∠B = 74. (The figure is not drawn to scale.)

99. Find the measure of value of AB for m∠P = 48. (The figure is not drawn to scale.)

100. Find the diameter of the circle for BC = 11 and DC = 27. Round to the nearest tenth.(The diagram is not drawn to scale.)

ID: A

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2nd Semester Exam Review - Geometry CPAnswer Section

1. B 2. B 3. C 4. A 5. B 6. A 7. 30 8. 11.6 9. yes; ∆EDF ∼ ∆BCA by SSS Similarity 10. x = 7,AB = 20

11. x = 32

, AB = 3

12. 45 13. 18 14. 6 15. 5 16. 15 17. 25 18. 2.3 19. x = 27, y = 52, z = 101 20. 61 21. 160 22. x = 7, NM = 21, OL = 21 23. x = 4, y = 6 24. x = 30, y = 60, z = 30 25. m∠1 = 90, m∠2 = 26, andm∠3 = 64 26. 8.5 27. 16 28. a = 110, b = 47 29. 54 30. 102 31. 25 32. 8

33. 40

3

34. ∆RST ∼ ∆UVW ; 5

6

35. 28.5 36. no 37. ∆ABC ∼ ∆MNO; SSS∼ 38. 80 ft

ID: A

2

39. 20 ft 40. 42.3 m 41. 7 42. 10

43. Yes, they form a Pythagorean triple; 122 + 352 = 372 and 12, 35, and 37 are all nonzero whole numbers.

44. 4 3 m 45. acute

46. 9 2 ft

47. 7 2 48. 16 m

49. 5 3

50. x = 13 3, y = 26 51. 89.12°

52. sinA = 810

, cosA = 610

53. 27.5 54. 4.8 55. 12.9 56. 11 57. 40.9 58. 7.9 59. w = 13.3, x = 10.2 60. 58 61. 37 62. 57 63. ∠1 is the angle of depression from airplane to the radar tower. 64. 39° 65. 483 in.2

66. 58.5 cm2

67. 70 in.2

68. 8

3 and

64

9

69. 991 m2

70. 5 :8; 5 :8 71. 5.9π cm 72. 9.61π m2

73. 450π cm2

74. 393.2 cm3

75. 224π in.3

76. 999 mm3

ID: A

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77. 1050 cm3

78. 2459.9 m3

79. 4189 mm3

80. no 81. 9 : 14 82. 3 : 7

83. 100 m2

84. 35 85. 67 86. 5 87. 66 88. 3.5 ft 89. 11.7 90. 38 91. 20.5 92. 32.5 93. 56 94. 84 95. 70 96. 18 97. 29 98. 32 99. 132 100. 55.3