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Geometry Semester Review Packet True or False. 1. Two lines always lie in the same plane. 2. There are lines which do not intersect each other. 3. If three points are collinear, then they are coplanar. 4. Any two points are collinear. 5. A line has two endpoints. 6. Given two points, there is more than one plane containing them. 7. If two complementary angles are congruent, then each is a right angle. 8. If AB and CD intersect at O, then mAOC = mBOD. 9. If mQ = 100, then Q does not have a complement. 10. If two angles have the same measure, then they are vertical angles. 11. Vertical angles are never supplementary. 12. The bisector of the vertex angle of an isosceles triangle bisects the base and is to the base. 13. The base angles of an isosceles triangle are acute. 14. An altitude of a triangle lies in the interior of the triangle. 15. If the three angles of a triangle have unequal measures, then no two sides of the triangle are congruent. 16. Two lines which are perpendicular to a third line are parallel. 17. Every right triangle has two acute angles. 18. The longest side of any triangle is called the hypotenuse. 19. The median of a triangle bisects the side to which it is drawn. 20. Each side of an angle is a ray. 21. The diagonals of a square are perpendicular to each other. 22. A square is a parallelogram. 23. If two consecutive angles of a quadrilateral are right angles, then the quadrilateral is a parallelogram. 24. If a diagonal of a parallelogram divides it into two isosceles triangles, the parallelogram is a rhombus. 25. If each pair of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. 26. Opposite angles of a parallelogram are congruent. 27. If the diagonals of a quadrilateral are perpendicular and congruent, then the quadrilateral is a square. 28. A diagonal of a parallelogram bisects two of its angles. 29. A quadrilateral with three right angles is a rectangle. 30. If a quadrilateral has a pair of opposite sides parallel and a pair of opposite sides congruent, then the quadrilateral is a parallelogram. Always, Sometimes or Never True 31. An equilateral triangle is isosceles. 32. An angle has a complement. 33. A ray has two endpoints. 34. An angle is equal to its supplement. 35. A right triangle is isosceles. 36. The complement of an acute angle is an obtuse angle. 37. Two lines perpendicular to a third line are skew. 38. Two skew lines are coplanar. 39. If two angles have a common side, the angles are adjacent. 40. The supplement of an obtuse angle is an obtuse angle. 41. Complementary angles are congruent to each other. 42. A ray has a midpoint. 43. Supplementary angles are adjacent. 44. Congruent angles are supplementary. 45. Theorems are reversible. 46. Three parallel lines are coplanar. 47. A square is a rectangle. 48. If the diagonals of a quadrilateral are perpendicular, then the quadrilateral is a rhombus. 49. The diagonals of a rectangle bisect each other. 50. A trapezoid with three congruent sides is isosceles. Problems 51. One of two supplementary angles is 8 more than the other. Find the measure of the larger angle. 52. Two consecutive angles of a parallelogram are in the ratio 7:5. Find the measure of the smaller angle. 53. The measures of the base angles of an isosceles triangle are 3x+5 and 5x25 and the measure of the vertex angle is 6x10. Find the measure of each angle. 54. Find the slope of the line through (5, 1) and (2, 7). 55. A line passes through (9, y) and (2, 6) and has slope 56. The vertices of RKC are R(8, 2), K(3, 9) and C(0, 4). Find the slope of the line through C that is parallel to RK . 57. The vertices of ATM are A(3, 1), T(1, 5) and M(1, 2). Find the slope of the altitude from T to AM . 58. What are the restrictions on the value of x in the figure at the right? x 9 . Find the value of y. 2 38 P 59. Given PM QT , PQ PT , mQ 3x 11 and mPMT 4 x 6 , find mQPT. Q 60. M T Find the area of a circle whose center is at the origin that passes through the point (7, 0). (Round to the nearest hundredth) 61. F Given FT EY , FE = 5x + 7, TY = 3x + 41 and TE = 5, find FT. T E Y a 62. Is a b? Show why! 63. In the figure, a b. (3x 18) a) If m7 = 100, find m3. 1 2 a b) If m7 = 96, find m6. (x + 58) b 8 7 c) If m1 = 120, find m5. 3 d) If m4 = 20, find m7. b 4 6 5 e) If m4 = 30, find m1. f) If m5 = 117, find m7. 64. Given AO BO and AZ BZ , what conclusion can A be made about OZ ? Why? O Z B B 65. In the diagram, 37 a) Find mADC A 60 35 b) Find mABC C 61 D 66. 116 Find mA. A 41 67. MTH is equilateral with MT = x + 8, TH = 2x 3 and MH = 3x 14. Find the perimeter of MTH. 68. If BD is an altitude of ABC, what conclusion must be true? Why? A D B a 69. If a b, find mNOT. b N O T (3x 18) (2x + 24) S 70. Given RS CD and CD bisects SCM, find mSCR. D 56 R 71. C M The ratio of the measure of 1:2 is 1:4. Find m2. 2 1 72. If AOC DOB, what conclusion must be true? Why? B A C O D C For each of the following, determine if the triangles can be proved congruent. If they can be proved congruent, give the reason (SSS, SAS, ASA, or HL). Otherwise, write NONE. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. Multiple Choice 85. Which of the following statements are always reversible. a) postulates 86. b) theorems c) definitions d) a & b Points M, P and O are collinear. If MO = 8, PO = 12 and MP = 4 then _?_ a) P lies between M and O c) M lies between P and O b) O lies between M and P d) none of these e) b & c 87. What can you assume from the diagram? a) EBC is a right angle D E b) points E, F and B are collinear F c) EFB is a straight angle d) CB DE C B A e) b & c 88. In the figure for #87, CD CB = _?_ b) DCB a) point C 89. b) A C b) 60 Subtract: b) 45 d) none of these c) 32 d) 30 e) none of these c) 144 d) 64 e) none of these 90 3917’42” a) 5043’18” 93. c) B C The ratio of the measures of 1 and 2 is 4:1. If 1 and2 form a straight angle find m1. a) 36 92. e) none of these The supplement of an angle is four times the complement. Find the measure of the angle. a) 120 91. d) CB If A is supplementary to B and C is supplementary to B, then _?_ a) A B 90. c) ABD b) 5042’17” c) 5142’18” d) 5042’18” Given BA BC , find mDBC. A a) 15b) 19 c) 28 e) none of these D 3x+5 d) 64 2x10 B C A 94. Given: AE is the bisector of FC , mF = 4x+30, mC = 2y+40, AF = y+5, AC = 3y5 Find mF 95. 96. a) 34 b) 50 c) 30 d) 26 F E C 2 and 5 are vertical angles. If m2 = 4x 18 and m5 = 2x + 26, find the value of x. a) 4 b) 14 c) 22 d) 44 If a b, name a pair of angles that are “not” congruent. 1 a 3 a) 1 and 2 b) 2 and 3 4 c) 3 and 4 97. b 2 d) 1 and 3 ABC is isosceles with base AC . If mA = x+14, mB = 7x1 and mC = 2x3. Find mB. a) 17 b) 31 c) 63 d) 118 e) none of these G Using the figure at the right, give the reason for each of the following. 98. a) multiplication d) defn midpoint 99. b) division e) cannot be proved C B D c) subtraction Given: CGD FGE Conclusion: CGE FGD a) addition d) multiplication 100. A Given: A and B are midpoints, AG BG Conclusion: CG FG b) subtraction e) cannot be proved c) substitution b) addition e) cannot be proved c) substitution Given: CG GF Conclusion: AC BF a) multiplication d) subtraction E F 101. A box contains five triangles, One is scalene, one is isosceles, two are equilateral and one is equiangular. If one triangle is selected at random, what is the probability that the triangle is isosceles? a) 1 5 b) 2 5 c) 3 5 d) 4 5 e) none of these A 102. In the figure, AC AD , B and E are midpoints. Which triangles can be proved congruent? a) ABD AEC b) BCD EDC c) BPC EPD d) a & b B e) none of these 103. C D The methods for proving that two lines are perpendicular are _?_ a) b) c) d) e) 104. E P two lines that form congruent adjacent angles two lines intersect to from right angles one line is the perpendicular bisector of the other a, b & c b&c In the figure, BD bisector of AC , AB = 5x+4, BC = 7x8 and AC = 3x+6. Find AD. A D a) 6 b) 12 c) 24 d) none of these B C a 105. If 2 6, which lines must be parallel? c 6 2 a) a and b c) none of these b) c and d d b 106. If ab, find m1. a b a) 50b) 110 (x + 20) c) 70 (2x + 10) 1 d) 150 e) none of these 107. In the figure, BX bisects ABC Find m1. A X a) 25b) 30 c) 20 1 2 d) 50 B 108. In a parallelogram, opposite angles are _?_ a) supplementary 109. 110. 111. 115 C b) complementary c) congruent d) acute The diagonals of a rhombus _?_ a) bisect opposite angles b) are congruent d) b & c e) a & c c) are perpendicular In an isosceles trapezoid, the _?_ a) diagonals are congruent, b) opposite angles are supplementary c) legs are congruent d) a, b & c If the diagonals of a quadrilateral bisect each other and are perpendicular, then the quadrilateral is a _?_ a) rectangle b) rhombus c) square d) trapezoid D 112. 113. If ABCD is a parallelogram, which of the following must be true? a) C D b) A C c) mB + mD = 180 d) AB BC If LUCK is a square, which of the following is NOT necessarily true. a) mLKU = 45 b) mKCU = 90 c) LU = UC d) LC KU e) all are true 114. Which of the following is not a property of an isosceles trapezoid? a) base angles are congruent b) opposite angles are supplementary c) legs are congruent d) diagonals are congruent e) all are properties of an isosceles trapezoid Problems 115. FGHJ is a parallelogram, FG = x+5, GH = 2x+3 mG = 40, mJ = 4x+12 F J a) Find mF b) Find the perimeter of FGHJ G H S 116. N SNOW is a square with mSON = 2x + 3 and YW = x 9. Find SO. Y W O Prove each of the following. C B F 117. Given: Prove: ABCD is a parallelogram: AF CE DF BE E D A A 118. Given: oO, AOB AOC Prove: B C O B C A 119. Given: Prove: AB CD : AB bisects CAD ACD is isosceles C B D T 120. Given: KOT is isosceles with base KT OPM T Prove: PM KT M O P K Geometry Answers to First Semester Review Packet 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. False True True True False True False True True False False True True 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. Always Sometimes Never Sometimes Sometimes Never Sometimes Never Sometimes Never Sometimes Never Sometimes 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. False True False True False True True True True False True 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. Sometimes Sometimes Sometimes Always Sometimes Always Always 94 75 50, 50, 80 8 3 37.5 7 11 4 3 38 < x < 180 58 153.93 87 25. True 26. True 27. False 28. False 29. True 30. False 54. 55. 56. 57. 58. 59. 60. 61. 62. No; lines do not form right angles 63. a) 100 b) 84 c) 120 d) 160 e) 150 f) 117 64. OZ is bis of AB 65. a) 144 b) 121 66. 105 67. 57 68. BD AC 69. 72 70. 68 71. 72 72. AOB DOC 73. HL 74. SAS 75. SSS, SAS 76. ASA, SAS 77. SAS 78. HL 79. ASA 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. E B B B C D C B C C D A A 100. 101. 102. 103. 104. 105. 106. 107. 108. 109. 110. E D D D B A B A C E D 80. SSS, SAS, ASA 81. None 111. B 112. B 82. ASA 113. E 83. 84. 85. 86. 114. E 115. a) 140 b) 58 116. 24 SAS None C C

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