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Name: _________________________ Midterm Review – Geometry PART I. True or False. If the statement is FALSE, write the word or phrase that will make the statement TRUE. 1. It is possible to have a triangle with sides of 10, 8, and 8. 2. In a triangle, the largest angle is opposite the longest side. 3. If the measure of one acute angles of a right triangle is 54, then the other acute angle is 46. 4. If AM = MB, then M must be the midpoint of AB. 5. When two parallel lines are cut by a transversal, corresponding angles are complementary. 6. If the legs of a right triangle are congruent, then each acute angle has a measure of 45. 7. Corresponding parts of congruent triangles are congruent. 8. Coplanar points are also collinear. 9. An equilateral triangle is isosceles. 10. On a line, if A is between B and C, then AB + BC = AC. 11. An obtuse triangle has three obtuse angles. 12. SSA is a method to prove a triangle congruent. 13. The intersection of two planes is a line. 14. The slopes of parallel lines are negative reciprocals of each other. 15. Acute angles are less than or equal to 90. 16. All equiangular triangles are equilateral. 17. If two lines have the same slope, then the lines are parallel. 18. If two lines intersect, then they intersect at a point. 19. The acute angles in a right triangle are supplementary. 20. If two angles are supplements of congruent angles, then the two angles are congruent. 21. All right triangles are congruent. 22. A right triangle has at least one right angle. 23. The hypotenuse of a right triangle is the side adjacent to the right angle. 24. All alternate interior angles are supplementary. 25. The base angles of an isosceles triangle are complementary. 26. Skew lines are coplanar lines that do not intersect. 27. The slope of a vertical line is zero. 28. The legs of an isosceles triangle are equal in length. 29. Two angles are complementary if the sum of their measures is 90. 30. The sum of the measures of the angles in a triangle is 360. 31. Adjacent angles form a linear pair. 32. AA is a method to prove triangles congruent. 33. An isosceles triangle has at least two congruent sides. 34. If a conditional statement is false, then so is its converse. 35. A scalene triangle has no congruent sides. 36. The hypotenuse of a right triangle is the side opposite the right angle. 37. The segment connecting the midpoints of the two sides of a triangle is parallel to the third side and half as long. 38. The leg of a right triangle is the longest side. 39. Two triangles are congruent if corresponding angles are congruent. 40. The contrapositive of the statement: “If a triangle is isosceles, then it has at least two congruent sides” is “If a triangle does not have at least two congruent sides, then it is not isosceles.” 41. Vertical angles are congruent. C PART II. Multiple Choice. 42. Plane X contains: A. CE B. Point C X C. Point D 43. Two segments that have equal length are: A. collinear B. congruent D. EB E B D C. coplanar D. perpendicular 44. On a number line, the distance between two points with coordinates –15 and 9 is: A. 6 B. –6 C. 23 D. –23 45. The statement “If mA = mB, then mB = mA” illustrates which property: A. reflexive B. symmetric C. transitive D. commutative 46. In the conditional statement p q , the q is called the: A. hypothesis B. conclusion C. deduction 47. The inverse of the statement “If it is snowing, then there is no school” is A. If there is no school, then it is snowing. B. There is no school if it is snowing. C. If it is not snowing, then there is school. D. There is no school only if it is not snowing. 48. The vertex of TRS is: A. R B. S C. T D. unknown D. converse 49. In the plane figure shown, 1 and 2 are: A. vertical angles B. nonadjacent angles C. complementary angles D. supplementary angles 50. mDEB + mAEB = A. mBEC B. mAEC C. mCED D. mAED 51. If EB bisects AEC, then mCEB = A. 45 B. 90 C. mDEC D. mAEC 52. If m DEC = 35, then m AED = A. 55 B. 145 C. 125 D. 155 53. If m 1 = 32 and m CED = 58, then 1 and CED are: A. vertical angles B. complementary angles C. supplementary angles D. obtuse angles Use the diagram on the right to answer questions 54-56. 54. If j k, then 8 is congruent to: A. 7 B. 3 C. 2 D. 1 55. If j k and t k, then m1 = A. m2 B. m3 C. m4 4 1 3 2 D. all three 56. If j k and m2 = 115, then 6 is: A. acute B. right C. obtuse 57. The number of right angles in a right triangle is: A. 0 B. 1 C. 2 6 5 7 8 D. unknown D. 3 58. The distance between (3, 5) and (9, -3) is: A. 100 B. 2 37 C. 2 35 D. 10 b4,6gand b2,8gis: 4,4g 3,1g C. b D. b 59. The midpoint of the segment with endpoints A. b6,2g B. b2,2g 60. In TQR, m T = 65 and m Q = 35, then m QRT = A. 80 B. 100 C. 10 D. 110 61. Determine which set of numbers can be the measure of the sides of a triangle. A. 7, 4, 3 B. 15, 11, 4 C. 24, 68, 43 D. 16, 18, 11 62. If m1 = 105, then m4 = A. 105 B. 75 C. 95 D. 65 63. Which of the following can NOT be used to prove that two triangles are congruent? A. SSS B. SSA C. SAS D. AAS 64. ABE CBE. In CBA which part of ABE corresponds to BEC? A. A B. EBA C. BCE D. BEA For #65-68, Use the diagram to determine the method that can be used to prove ABCEDC. 65. Given BD; BC DC. A. SSS B. SAS C. ASA D. AAS 66. Given BC DC; AC EC. A. AAS B. SSS C. SAS D. ASA 67. Given A and E are right angles, BC DC. A. HL B. AAS C. SSS D. SSA 68. Given AB DE, AC EC and A and E are right angles. A. AAS B. SSS C. SAS D. HL 69. The measure of one base angle of an isosceles triangle is 47. Find the measure of the vertex angle. A. 86 B. 47 C. 106 D. 53 70. In isosceles DEF, DE = EF. If DE = 3x – 6, DF = 2x + 2, and EF = x + 4, find the length of DF. A. 7 B. 9 C. 12 D. 5 71. K and J are complementary angles. If m K = 54, find m J. A. 71 B. 161 C. 90 D. 36 72. P and Q form a linear pair and m P = 62. Find m Q. A. 62 B. 28 C. 118 D. 90 73. Identify the if-then form of “All tigers are cats.” A. If the animal is a tiger, then it is a cat. B. If the animal is a cat, then it is a tiger. C. If the animal is not a cat, then it is not a tiger. D. If the animal is not a tiger, then it is not a cat. 74. In ABC, m A = 60 and m ACB = 70. What is the longest side of ABC? A. unknown B. AC C. BC D. AB k Use the figure on the right for questions 75 – 78. Write the answer in the blank provided. j 1 2 4 3 75. 8 and 6 are _______________ A. complementary B. congruent C. unknown D. supplementary 5 8 6 7 9 12 10 11 76. If k j and m2 = 72, then m4 = _______________ A. 108 B. 72 C. 180 D. 910 77. If k j, m9 = 9x + 5, and m8 = x + 35, then x = __________ A. 140 B. 5 C. 14 D. 180 78. Given m10 = 5x + 2 and m6 = 3x + 28, find x so that k j. A. 13 B. 12 C. 9 D. 8 79. The measures of two angles of a triangle are 32 and 47. What is the measure of the third angle? A. 79 B. 109 C. 180 D. 101 80. Find the values of x and y so that ABC DEF by HL. A. x=45, y=12 B. x=45, y=5 C. x=90, y=12 D. x=90, y=13 81. Two sides of a triangle have lengths 14 and 19. Which measurement could be the measure of the third side? A. 4 B. 6 C. 33 D. 35 82. What conclusion is justified by the following statements: “If I get a job, then I will save money.” and “If I save money, then I will buy a car.”? A. If I get a job, then I will buy a car. B. If I buy a car, then I will get a job. C. I can buy a car, if I get a job. D. If I save my money, then I will buy a car. 83. The contrapositive of r q is: A. r q B. r q C. r q D. none of these 84. The lengths of the legs of an isosceles triangle are 3x and x + 12. Find x. A. 18 B. 12 C. 6 D. 4 85. An angle has a measure of x. Its complement has a measure x + 10. Find x. A. 80 B. 45 C. 50 D. 40 86. An angle and its supplement have measures x + 20 and x – 20. Find the measure of each angle. A. 90o and 90o B. 80o and 100o C. 120o and 60o D. 110o and 70o 87. Find the distance between A b3,4gand C b7,2g. Reduce to simplest radical form. A. 18 B. 3 6 C. 168 D. 2 34 88. In the figure, if AD = 50, CD = 12, and B is the midpoint of AC, find BC. A. 38 • • • • A B C D B. 19 C. 25 D. 37 89. What is the slope of the line that passes through the points (-4, 8) and (3, -7)? A. 7 15 B. 15 7 C. - 15 7 D. 1 7 90. Find the slope of the line perpendicular to the line containing points (4,5) and (-2,3). A. ½ B. –1/3 C. -3 D. 1/3 91. List the sides of STU in order from LONGEST to SHORTEST if the angles of STU have the indicated measures: m S = x + 6; m T = 2x + 8; and m U = 3x –2. A. ST-SU-TU B. TS-UT-SU C. US-UT-ST D. TU-US-ST 92. The measures of two vertical angles are 5x–15 and 3x+3. Find x. A. 14 B. 16 C. 12 D. 9 93. The measures of the angles of a triangle are x – 15, x, and x + 15. Find x. A. 60 B. 55 C. 65 D. 45 94. The side opposite the right angle in a right triangle is called the________________________. A. base B. vertex C. hypotenuse D. leg 95. A triangle with no congruent sides is called a(n) ______________ triangle. A. equiangular B. isosceles C. obtuse D. scalene