Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Name: ________________________ Class: ___________________ Date: __________ ID: A 2nd Semester Exam Review - Geometry CP 3. Which statement can you use to conclude that quadrilateral XYZW is a parallelogram? 1. Complete this statement: A polygon with all sides the same length is said to be ____. a. regular b. equilateral c. equiangular d. convex 2. WXYZ is a parallelogram. Name an angle congruent to ∠WXY. a. b. c. d. WZ ≅ XY and XW ≅ WZ WZ ≅ ZY and XW ≅ YZ WZ ≅ XY and XW ≅ YZ WN ≅ NZ and YN ≅ NX 4. Classify the figure in as many ways as possible. a. b. c. d. ∠WZX ∠WZY ∠YZX ∠XYZ a. b. c. d. rectangle, square, quadrilateral, parallelogram, rhombus rectangle, square, parallelogram rhombus, quadrilateral, square square, rectangle, quadrilateral 5. The two rectangles are similar. Which is the correct proportion for corresponding sides? a. 12 8 = 24 4 b. 12 4 = 24 8 c. 12 4 1 = 8 24 d. 4 12 = 24 8 Name: ________________________ ID: A 7. Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale. 6. a. b. c. d. 13.27 17.55 10.58 176 8. AB = 15, BC = 9, and CD = 10 2 Name: ________________________ ID: A Determine whether each pair of triangles is similar. Justify your answer. 9. Find x and the measures of the indicated parts. 10. AB 11. AB 12. If m∠BDC = 35, m arc AB = 100, and m arc CD = 100, find m∠1. 3 Name: ________________________ ID: A Find x. Assume that any segment that appears to be tangent is tangent. 13. 16. If m∠1 = 2x + 2, m∠2 = 9x, find m∠1. 14. Find x. Assume that segments that appear tangent are tangent. 17. 15. Find x. Assume that segments that appear tangent are tangent. 4 Name: ________________________ ID: A 21. For the parallelogram, if m∠2 = 5x − 30 and m∠4 = 3x − 10, find m∠3. The diagram is not to scale. Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent. 18. 22. LMNO is a parallelogram. If NM = x + 14 and OL = 2x + 7, find the value of x and then find NM and OL. 19. Find the values of the variables in the parallelogram. The diagram is not to scale. 23. Find values of x and y for which ABCD must be a 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. 5 Name: ________________________ ID: A 27. In quadrilateral ABCD, AE = x + 14 and BE = 3x − 18 . For what value of x is ABCD a rectangle? 24. In the rhombus, m∠1 = 3x, m∠2 = x + y, and m∠3 = 3z. Find the value of each variable. The diagram is not to scale. 28. Find the values of a and b.The diagram is not to scale. 25. Find the measure of the numbered angles in the rhombus. 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. 26. In rectangle KLMN, KM = 5x + 16 and LN = 58.5. Find the value of x. 30. LM is the midsegment of ABCD. AB = 85 and DC = 119. What is LM? 6 Name: ________________________ ID: A ABCD. 31. LM is the midsegment of AB = x + 8, LM = 4x + 3, and DC = 173. What is the value of x? What is the solution of each proportion? 32. 3 a = 15 33. 40 3y − 8 12 = y 5 Are the polygons similar? If they are, write a similarity statement and give the scale factor. 34. 7 Name: ________________________ ID: A The polygons are similar, but not necessarily drawn to scale. Find the value of x. 36. Are the triangles similar? How do you know? 35. 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. 8 Name: ________________________ ID: A 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. 9 Name: ________________________ ID: A Find the length of the missing side. Leave your answer in simplest radical form. 47. Find the length of the leg. If your answer is not an integer, leave it 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. 48. The area of a square garden is 128 m2. How long is the diagonal? 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. Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form. 51. Find the missing value to the nearest hundredth. 49. 52. Write the ratios for sin A and cos A. 50. 10 Name: ________________________ ID: A Use a trigonometric ratio to find the value of x. Round your answer to the nearest tenth. 54. 53. Find the value of x. Round to the nearest tenth. 55. 58. 56. 59. Find the value of w, then x. Round lengths of segments to the nearest tenth. 57. 11 Name: ________________________ ID: A Find the value of x. Round to the nearest degree. 61. 60. 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? 12 Name: ________________________ ID: A Find the area. The figure is not drawn to scale. 66. 65. 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 m 2 . 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. 13 Name: ________________________ ID: A 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. 14 Name: ________________________ ID: A 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. Find the volume of the square pyramid shown. Round to the nearest tenth if necessary. 77. 76. Find the volume of the composite space figure to the nearest whole number. 15 Name: ________________________ ID: A 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. 82. Find the similarity ratio of a cube with volume 216 ft 3 to a cube with volume 2744 ft 3 . 83. The volumes of two similar solids are 729 m 3 and 125 m 3 . The surface area of the larger solid is 324 m 3 . What is the surface area of the smaller solid? 81. Find the similarity ratio of a prism with the surface area of 81 m 2 to a similar prism with the surface area of 196 m 2 . 16 Name: ________________________ ID: A 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 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. 85. m∠P = 23 88. NA ≅ PA , MO ⊥ NA, RO ⊥ PA , MO = 7 ft What is PO? 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. 17 Name: ________________________ ID: A Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale. 92. Find x. (The figure is not drawn to scale.) 89. 90. 93. Find m∠BAC. (The figure is not drawn to scale.) 91. Find the measure of ∠BAC. (The figure is not drawn to scale.) 18 Name: ________________________ ID: A 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.) 19 Name: ________________________ ID: A 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.) 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.) 20 ID: A 2nd Semester Exam Review - Geometry CP Answer Section 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. B B C A B A 30 11.6 yes; ∆EDF ∼ ∆BCA by SSS Similarity x = 7, AB = 20 3 x = , AB = 3 2 45 18 6 5 15 25 2.3 x = 27, y = 52, z = 101 61 160 x = 7, NM = 21, OL = 21 x = 4, y = 6 x = 30, y = 60, z = 30 m∠1 = 90, m∠2 = 26, and m∠3 = 64 8.5 16 a = 110, b = 47 54 102 25 8 40 3 34. ∆RST ∼ ∆UVW ; 35. 36. 37. 38. 5 6 28.5 no ∆ABC ∼ ∆MNO; SSS∼ 80 ft 1 ID: A 39. 40. 41. 42. 20 ft 42.3 m 7 10 43. Yes, they form a Pythagorean triple; 12 2 + 35 2 = 37 2 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° 8 6 , cos A = 52. sin A = 10 10 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 8 64 68. and 3 9 69. 70. 71. 72. 991 m 2 5 : 8; 5 : 8 5.9π cm 9.61π m2 73. 450π cm 2 74. 393.2 cm 3 75. 224π in. 3 76. 999 mm 3 2 ID: A 77. 1050 cm 3 78. 2459.9 m 3 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 4189 mm 3 no 9 : 14 3:7 100 m 2 35 67 5 66 3.5 ft 11.7 38 20.5 32.5 56 84 70 18 29 32 132 55.3 3