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1 Class: Date: 2nd Semester Exam Review - Geometry CP 1. Complete this statement: A polygon with all sides the same length is said to be. a. regular b. equilateral c. equiangular d. convex 3. Which statement can you use to conclude that quadrilateral XYZW is a parallelogram? 2. WXYZ is a parallelogram. Name an angle congruent to WXY. a. WZ XY and XW WZ b. WZ ZY and XW YZ c. WZ XY and XW YZ d. WN NZ and YN NX 4. Classify the figure in as many ways as possible. a. WZX b. WZY c. YZX d. XYZ 5. The two rectangles are similar. Which is the correct proportion for corresponding sides? a. rectangle, square, quadrilateral, parallelogram, rhombus b. rectangle, square, parallelogram c. rhombus, quadrilateral, square d. square, rectangle, quadrilateral a = 24 4 b = 24 8 c = 8 24 d =

2 Determine whether each pair of triangles is similar. Justify your answer AB Find x and the measures of the indicated parts. 8. AB 9. If m BDC = 35, m arc AB = 100, and m arc CD = 100, find m 1. 2

3 10. Find x. Assume that any segment that appears to be tangent is tangent. 13. If m 1 = 2x + 2, m 2 = 9x, find m Find x. Assume that segments that appear tangent are tangent Find x. Assume that segments that appear tangent are tangent. 15. Find the values of the variables in the parallelogram. The diagram is not to scale. 3

4 16. In the parallelogram, m QRP = 57 and m PRS = 62. Find m PQR. The diagram is not to scale. 19. Find values of x and y for which ABCD must be a parallelogram. The diagram is not to scale. 17. For the parallelogram, if m 2 = 5x 30 and m 4 = 3x 10, find m 3. The diagram is not to scale. 20. 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. 18. LMNO is a parallelogram. If NM = x + 14 and OL = 2x + 7, find the value of x and then find NM and OL. 21. Find the measure of the numbered angles in the rhombus. The diagram is not to scale. 4

5 22. In rectangle KLMN, KM = 5x + 16 and LN = Find the value of x. 25. J and M are base angles of isosceles trapezoid JKLM. If m J = 15x + 6, and m M = 14x + 14, find m K. 26. LM is the midsegment of ABCD. AB = 85 and DC = 119. What is LM? 23. In quadrilateral ABCD, AE = x + 14 and BE = 3x 18. For what value of x is ABCD a rectangle? 27. LM is the midsegment of ABCD. AB = x + 8, LM = 4x + 3, and DC = 173. What is the value of x? 24. Find the values of a and b.the diagram is not to scale. What is the solution of each proportion? 28. 3y 8 12 = y 5 5

6 Are the polygons similar? If they are, write a similarity statement and give the scale factor. 29. The polygons are similar, but not necessarily drawn to scale. Find the value of x. 31. Are the triangles similar? How do you know? 30. State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used

7 33. 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. 34. 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. 35. 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

8 Find the length of the missing side. Leave your answer in simplest radical form Find the length of the leg. If your answer is not an integer, leave it in simplest radical form. 38. A triangle has side lengths of 38 in, 22 in, and 39 in. Classify it as acute, obtuse, or right. 39. 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. 41. The area of a square garden is 128 m 2. 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 Find the missing value to the nearest hundredth. 45. Write the ratios for sin A and cos A

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

10 Find the value of x to the nearest degree 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? Find the area. The figure is not drawn to scale Find the area of the trapezoid. Leave your answer in simplest radical form. 59. Find the circumference. Leave your answer in terms of π. 10

11 Find the area of the circle. Leave your answer in terms of π. 60. Find the surface area of the cylinder in terms of π. 61. Find the volume of the given prism. Round to the nearest tenth if necessary

12 Find the volume of the cylinder in terms of π. 63. Find the volume of the square pyramid shown. Round to the nearest tenth if necessary Find the volume of the cone shown as a decimal rounded to the nearest tenth. 66. Find the volume of the sphere shown. Give each answer rounded to the nearest cubic unit. 12

13 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.) 67. m O = 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. 68. m P = NA PA, MO NA, RO PA, MO = 7 ft What is PO? 69. 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. 13

14 Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale Find x. (The figure is not drawn to scale.) Find m BAC. (The figure is not drawn to scale.) 74. Find the measure of BAC. (The figure is not drawn to scale.) 14

15 77. m R = 42. Find m O. (The figure is not drawn to scale.) 78. If mby = 40, what is m YAC? (The figure is not drawn to scale.) 79. mde = 106 and mbc = 70. Find m A. (The figure is not drawn to scale.) 15

16 80. Find the value of x for mab = 31 and mcd = 27. (The figure is not drawn to scale.) 83. B is the midpoint of AC, D is the midpoint of CE, and AE = 21. Find BD. The diagram is not to scale. 81. Find m D for m B = 74. (The figure is not drawn to scale.) a. 42 b. 21 c d Points B, D, and F are midpoints of the sides of ACE. EC = 30 and DF = 23. Find AC. The diagram is not to scale. 82. Find the measure of value of AB for m P = 48. (The figure is not drawn to scale.) a. 30 b c. 60 d

17 85. Find the value of x. 87. DF bisects EDG. Find the value of x. The diagram is not to scale. a. 4 b. 8 c. 6.6 d Q is equidistant from the sides of TSR. Find the value of x. The diagram is not to scale. a b. 90 c. 30 d Which statement can you conclude is true from the given information? Given: AB is the perpendicular bisector of IK. a. 27 b. 3 c. 15 d. 30 a. AJ = BJ b. IAJ is a right angle. c. IJ = JK d. A is the midpoint of IK. 17

18 89. In ABC, G is the centroid and BE = 9. Find BG and GE. 90. Name a median for ABC. a. BG = 2 1 4, GE = 63 4 b. BG = 3, GE = 6 c. BG = 6, GE = 3 a. AD b. CE c. AF d. BD d. BG = 4 1 2, GE = Name the point of concurrency of the angle bisectors. a. A b. B c. C d. not shown 18

19 92. For a triangle, list the respective names of the points of concurrency of perpendicular bisectors of the sides bisectors of the angles medians lines containing the altitudes. a. incenter circumcenter centroid orthocenter b. circumcenter incenter centroid orthocenter c. circumcenter incenter orthocenter centroid d. incenter circumcenter orthocenter centroid 93. Where can the medians of a triangle intersect? I. inside the triangle II. on the triangle III. outside the triangle a. I only b. III only c. I or III only d. I, II, or II 94. Which diagram shows a point P an equal distance from points A, B, and C? a. b. c. d. 19

20 95. Name the smallest angle of ABC. The diagram is not to scale. a. A b. C c. Two angles are the same size and smaller than the third. d. B 96. List the sides in order from shortest to longest. The diagram is not to scale. 98. Which three lengths can NOT be the lengths of the sides of a triangle? a. 23 m, 17 m, 14 m b. 11 m, 11 m, 12 m c. 5 m, 7 m, 8 m d. 21 m, 6 m, 10 m 99. Two sides of a triangle have lengths 10 and 18. Which inequalities describe the values that possible lengths for the third side? a. x 8 and x 28 b. x > 8 and x < 28 c. x > 10 and x < 18 d. x 10 and x m A = 9x 7, m B = 7x 9, and m C = 28 2x. List the sides of ABC in order from shortest to longest. a. AB; AC; BC b. BC ; AB; AC c. AC; AB; BC d. AB; BC ; AC a. LK, LJ, JK b. LJ, LK, JK c. LJ, JK, LK d. LK, JK, LJ 97. Which three lengths could be the lengths of the sides of a triangle? a. 12 cm, 5 cm, 17 cm b. 10 cm, 15 cm, 24 cm c. 9 cm, 22 cm, 11 cm d. 21 cm, 7 cm, 6 cm 20

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