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NAME _____________________________________________ DATE ____________________________ PERIOD _____________ Geometry Final Exam Review 2014-2015 Write the letter for the correct answer in the blank at the right of each question. For Questions 1-4, refer to the figure. 1. Name a median. A π π B β‘ππ C ππ D π π Μ Μ Μ Μ H ππ J π π β‘ B ππ Μ Μ Μ Μ C ππ D π π G Μ Μ Μ Μ π π H Μ Μ Μ Μ ππ J π π 2. Name an angle bisector. Μ Μ Μ Μ Μ F π π β‘ G ππ 3. Name a perpendicular bisector. Μ Μ Μ Μ Μ A π π 4. Name an altitude. F Μ Μ Μ Μ Μ π π For Questions 5-7, refer to the figure to determine which is a true statement for the given information. 5. Μ Μ Μ Μ πΉπΊ is an altitude. A β DGF is a right angle. B DF = EF C DG = GE D β DFG β β EFG 6. Μ Μ Μ Μ πΉπΊ is a median. F β DGF is a right angle. G DF = EF H DG = GE J β DFG β β EFG Μ Μ Μ Μ is an angle bisector. 7. πΉπΊ A β DGF is a right angle. B DF = EF C DG = GE D β DFG β β EFG 8. Name the longest side of β³ABC. F Μ Μ Μ Μ π΄π΅ G Μ Μ Μ Μ π΅πΆ H Μ Μ Μ Μ π΄πΆ J cannot tell 9. Name the angle with the greatest measure in β³GHI. A β G B β H C β I D cannot tell 10. Carrie, Maria, and Nayla are friends that live close to one another. Which two friends have the shortest distance between them? A Maria and Nayla B Carrie and Maria C Carrie and Nayla D All three live equal distances from each other. 11. Find the possible values for mβ 1. F mβ 1 = 124 G 0 < mβ 1 < 5 H 90 > mβ 1 > 56 J 180 > mβ 1 > 56 12. Which of the following sets of numbers can be the lengths of the sides of a triangle? A 12, 9, 2 B 11, 12, 23 C 2, 3, 4 D β3,β5,β18 13. If point E is the centroid of β³ABC, BD = 12, EF = 7, and AG = 15, find ED. 14. List the angles of β³GHI in order from largest to smallest measure. 15. List the sides of β³PQR in order from longest to shortest. 16. Find x in β³PQR. A 13 B 15 C 16 D β60 G8 H β32 J β514 17. Find x in β³STU. F2 18. Which set of measures could represent the lengths of the sides of a right triangle? A 2, 3, 4 B 7, 11, 14 C 8, 10, 12 D 9, 12, 15 19. Find x in β³DEF. F6 G 6β2 H 6β3 J 12 B 15β3 C 15 D 30 19. Find y in β³XYZ. A 7.5β3 20. The length of the sides of a square is 10 meters. Find the length of the diagonals of the square. F 10 m G 10β2 m H 10β3 m 21. Find x in β³HJK. A 5 β2 22. Find x in β³ABC. F 25 B 5 β3 C 10 D 15 G 25β2 H ππβ3 J 100 C 18.4 D 47.1 23. Find x to the nearest tenth. A 7.3 B 17.3 J 20 m 24. Find the measure of the angle of elevation of the Sun when a pole 25 feet tall casts a shadow 42 feet long. F 30.8° G 36.5° H 53.5° J 59.2° 25. Which is the angle of depression in the figure at the right? A β AOT B β AOB C β TOB D β BTO Solve for each missing variable. 26. 27. x = _________ 28. x = _________ 29. x = _________ x = _________ 30. x = _________ y = _________ 31. A 38-foot tree casts a 16-foot shadow. Find the measure of the angle of elevation of the sun to the nearest degree. 32. A boat is 2000 meters from a cliff. If the angle of depression from the top of the cliff to the boat is 10°, how tall is the cliff? Round your answer to the nearest tenth. 32. A plane flying at an altitude of 10,000 feet begins descending when the end of the runway is 60,000 feet from a point on the ground directly below the plane. Find the measure of the angle of descent (depression) to the nearest degree. 33. Given B(β4, β6), under which reflection is Bβ²(4, β6)? A reflected in the x-axis B reflected in the y-axis C reflected in the line y = β2 D reflected in the line y = x 34. Which transformation turns every point of the preimage through a specified angle and direction about a fixed point? F reflection G rotation H translation J dilation 35. What kind of transformation is represented in the figure at the right? A translation B rotation C reflection D dilation Μ Μ Μ Μ with endpoints C(5, β7) and D(β3, 9) is rotated 270° about the origin. What is the coordinate of 36. The line segment πΆπ· D'? A D'(β3, β9) B D'(3, β9) C D'(9, β3) D D'(9, 3) H A'(6, 1) J A'(β1, 6) 37. Find the reflection of the point A(6, β1) in the x-axis. F A'(6, β1) G A'(β6, 1) 38. Graph β³TUV with vertices T(3, 3), U(6, β1), and V(β2, 1). Then graph the image of β³TUV reflected in the line y = 2. y 10 9 8 7 6 5 4 3 2 1 β10 β9 β8 β7 β6 β5 β4 β3 β2 β1 β1 β2 β3 β4 β5 β6 β7 β8 β9 β10 39. Find the sum of the measures of the interior angles of a convex 45-gon. A 8100 B 7740 C 360 D 172 G 66 H 102 J 138 40. Find the value of x. F 30 41. Find the sum of the measures of the exterior angles of a convex 39-gon. A 39 B 90 C 180 D 360 42. Which of the following is a property of a parallelogram? F Each pair of opposite sides is congruent. G Only one pair of opposite angles is congruent. H Each pair of opposite angles is supplementary. J There are four right angles. 1 2 3 4 5 6 7 8 9 10 x 43. For parallelogram ABCD, find mβ 1. A 60 B 54 C 36 D 18 44. ABCD is a parallelogram with diagonals intersecting at E. If AE = 3x + 12 and EC = 27, find the value of x. F5 G 17 H 27 J 47 45. Find the values of x and y so that this quadrilateral is a parallelogram. A x = 13, y = 24 B x = 13, y = 6 C x = 7, y = 24 D x = 7, y = 6 46. Find the value of x so that this quadrilateral is a parallelogram. F 12 G 24 H 36 J 132 47. Parallelogram ABCD has vertices A(8, 2), B(6, β4), and C(β5, β4). Find the coordinates of D. A D(β5, 2) B D(β3, 2) C D(β2, 2) D D(β4, 8) 48. ABCD is a rectangle. If AC = 5x + 2 and BD = x + 22, find the value of x. F5 G6 H 11 J 26 49. Which of the following is true for all rectangles? A The diagonals are perpendicular. B The diagonals bisect the angles. C The consecutive sides are congruent. D The consecutive sides are perpendicular 50. ABCD is a rectangle with B(β4, 6), C(β4, 2), and D(10, 2). Find the coordinates of A. F A(6, 4) G A(10, 4) H A(2, 6) J A(10, 6) C 68 D 90 51. For rhombus GHJK, find mβ 1. A 22 B 44 52. The diagonals of square ABCD intersect at E. If AE = 2x + 6 and BD = 6x β 10, find AC. F 11 G 28 H 56 J 90 53. ABCD is an isosceles trapezoid with A(10, -1), B(8, 3), and C(-1, 3). Find the coordinates of D. A D(β3, β1) B D(β10, β11) C D(β1, 8) D D(β3, 3) 54. For isosceles trapezoid MNOP, find mβ MNP. F 44 G 64 H 80 J 116 55. The length of one base of a trapezoid is 19 inches and the length of the median is 16 inches. Find the length of the other base. A 35 in. B 19 in. C 17.5 in. D 13 in 56. Judith built a fence to surround her property. On a coordinate plane, the four corners of the fence are located at (β16, 1), (β6, 5), (4, 1), and (β6, β3). Which of the following most accurately describes the shape of Judithβs fence? F square G rectangle H rhombus J trapezoid 57. For kite PQRS, find mβ S. A 248 B 68 Solve. 58. C 112 D 124 59. x = _______ 60. x = _______ x = _______ Solve. Each figure is a parallelogram. 61. x = ______ y = ______ z = ______ 62. x = ______ y = ______ z = ______ 63. x = ______ y = ______ z = ______ 64. Determine whether ABCD is a parallelogram. Justify your answer. 65. The length of the median of trapezoid EFGH is 13 feet. If the bases have lengths 2x + 4 and 10x β 50, find x. 66. ABCD is a kite, If RC = 10, and BD = 48, find CD. 67. Of the 300 television sets sold at an electronics store last month, 90 were flat-screen TVs. What is the ratio of flatscreen TVs to other TVs sold last month? 68. Determine whether β³ABC βΌ β³DEF. Justify your answer. 69. When a 5-foot vertical pole casts a 3-foot 4-inch shadow, an oak tree casts a 20-foot shadow. Find the height of the tree. 2 70. Quadrilateral ABCD βΌ quadrilateral WXYZ, AB = 15, BC = 27, BC = 27, and the scale factor of WXYZ to ABCD is . 3 Find XY. 1 71. The blueprint for a swimming pool is 8 inches by 2 2 inches. The actual pool is 136 feet long. Find the width of the pool. 72. Find CD. 73. If quadrilateral ABCD βΌ quadrilateral PQRS, find BC. 74. β³ABC βΌ β³XYZ, AB = 12, AC = 16, BC = 20, and XZ = 24. Find the perimeter of β³XYZ. For Questions 75 and 76, use the figure. 75. Identify the similar triangles. 76. Find the value of x. 77. The ratio of the measures of the three sides of a triangle is 3:4:6. If the perimeter is 91, find the length of the longest side. 78. If β³RST βΌ β³UVW, find mβ W. 79. Find the value of y so that ππ || π΅πΆ. 80. Find the value of x. For Questions 81-83, use the figure to the right. 81. Name a radius. A Μ Μ Μ Μ ππ΅ B Μ Μ Μ Μ π΄π΅ C Μ Μ Μ Μ π΅πΆ D β‘π΄πΆ Μ Μ Μ Μ Μ G ππΆ Μ Μ Μ Μ H π΅πΆ β‘ D π΄πΆ B Μ Μ Μ Μ Μ π΅πΆ C β‘π΄πΆ D β‘π΅π· 82. Name a chord. F Μ Μ Μ Μ ππ΅ 83. Name a tangent. A Μ Μ Μ Μ π΄π΅ 84. The wheels on Elliotβs truck each have a circumference of 22 inches. Determine the radius of each wheel to the nearest length. F 2.5 in. G 3.5 in. H 5 in. J 7 in. Μ = 72. Find mβ BCD. 85. In β¨C, mπ΄π΅ A 72 B 108 C 144 D 180 Μ in β¨R to the nearest hundredth. 86. Find the length of ππ F 9.42 m G 4.71 m H 3.14 m J 1.57 m 87. Find YB if the diameter of β¨A is 10 inches, the diameter of β¨B is 8 inches, and AX = 3 inches. 88. Find the radius and diameter of a flying disc with a circumference of 11Ο inches. Μ. 89. In β¨K, mβ HKG = x + 10 and mβ IKJ = 3x β 22. Find m πΉπ½ 90. The diameter of β¨C is 18 units long. Find the length of an arc that has a measure of 100. Round to the nearest hundredth.