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Geometry 235 Semester 1 Exam – Part 1 DO NOT WRITE ON THIS COPY OF THE EXAM For questions 1 - 20, match the symbol or term in column A with the correct name or definition in column B. Column A Column B 1. A. segment 2. B. two angles that share a common side and vertex with no interior points in common 3. C. parallel 4. D. congruent 5. E. angle 6. F. an angle with measure of 7. G. perpendicular 8. acute angle H. two angles whose sides form two pairs of opposite rays 9. obtuse angle I. the basic unit to measure the size of an angle 10. complementary angles J. an angle with a measure between 11. right angle K. two lines in the same plane that never intersect 12. perpendicular lines L. 13. supplementary angles M. 14. parallel lines N. 15. vertical angles O. two angles whose measures have a sum of 16. degree P. 17. adjacent angles Q. 18. Pythagorean theorem R. line 19. Midpoint formula S. two lines that intersect to form a right angle 20. Distance formula T. two angles whose measures have a sum of and an angle with a measure less than ray For questions 21 - 27, use the figure below to answer the questions. 21. Name a point collinear with . 22. Name a line shown in the figure. 23. Name a segment that has B as an endpoint. 24. Name a ray that has C as an endpoint. 25. Does pass through C? 26. Is A on ? 27. Name an acute angle. For questions 28 – 35 use the figure below. Don’t forget to use the 28. Name an acute angle with symbol. as a side. 29. Name an obtuse angle with as a side. 30. Name a straight angle. 31. Name a right angle. 32. Name a pair of vertical angles. 34. Name an angle complementary to For questions 36 – 37, questions. bisects 36. . and 33. Name an angle adjacent to angle . 35. Name an angle supplementary to . . Use the figure at the right to answer the 37. For questions 38 - 46, use the figure at the right to answer the questions. 38. Name a right angle. 39. Name the vertex of . 40. Name a side of 41. Another name for 42. Another name for . . 43. A pair of opposite rays. 45. is what type of angle? (acute, obtuse, straight or right) 46. is what type of angle? (acute, obtuse, straight or right) 44. A pair of perpendicular rays. For questions 47 - 48, find the measure of the complement and supplement of the given angle. 47. 48. For questions 49 – 50, bisects . Find the value of x. 49. 50. For questions 51 - 54, name each of the following. 51. An angle congruent to 1 52. An angle congruent to 3 53. An angle supplementary to 5 54. An angle corresponding to 2 For questions 55 – 58, find the measure of each angle. 55. 56. 57. 58. For questions 59 – 66, find the measure of each angle. 59. 60. 61. 62. 63. 64. 65. 66. Use the figure at the below to answer questions 67 – 77. 67. a vertical angle to . 68. an interior angle on the same side of the transversal as . 69. an exterior angle on the same side of the transversal as . 70. an alternate interior angle with 71. a corresponding angle to 72. If 74. If 76. If and 77. If and . . , then , then 73. If , then 75. If , then , then x , then x For questions 78 and 79, Classify each triangle by its sides and by its angles. 78. 79. For questions 80 - 90, answer True or False: 80. Every triangle is equiangular. 81. An obtuse triangle contains two obtuse angles. 82. An equilateral triangle has no congruent sides. 83. A right triangle has one right angle. 84. A scalene triangle has no congruent sides. 85. A horizontal line has a slope of 0. 86. Parallel lines have the same slope. 87. A vertical line has a slope of 0. 88. If two parallel lines are cut by a transversal, same-side interior angles are congruent. 89. The slopes of perpendicular lines are reciprocals of each other. 90. If two parallel lines are cut by a transversal, alternate exterior angles are supplementary. For questions 91 - 94, Identify the following for the figure shown. 91. the legs 92. the vertex angle 93. the base 94. a base angle For questions 95 - 98, you know that the indicated parts of the triangles are congruent. Which postulate or theorem, if any, could you use to prove that If one is not possible, write NP. 95. 96. 97. 98. For questions 99 - 101, Complete the following congruence statements. 99. 100. 101. For questions 102 - 106, Fill in the blanks. base equiangular equilateral right legs scalene isosceles vertex 102. The non-congruent side of an isosceles triangle is called the . 103. A triangle with two sides congruent is called a(n) _____________________________ triangle. 104. A triangle with all sides congruent is an equilateral triangle and also a(n) ___________________ triangle. 105. A triangle with no congruent sides is called a(n) 106. The angle formed by the congruent sides of an isosceles triangle is called the triangle. angle. For questions 107 - 111, find the value of 107. 108. 110. 111. in each of the following triangles. 109. State the missing congruence statement that is needed to prove that theorem. 112. Given: Using the SAS Congruence Postulate. 113. Given: Using the AAS Congruence Postulate. 114. Given: Using the ASA Congruence Postulate. 115. Given: Using the SSS Congruence Postulate. 116. Given: Using the HL Congruence Theorem. using the given postulate or For questions 117 - 122. state whether you would use ASA, SSS, SAS, AAS, HL, or none to prove the triangles are congruent. 117. 118. 119. 120. 121. 122. 123. Use the distance formula to find the length of the segment with endpoints 124. Find the midpoint of the line segment with endpoints . . 125. Find the slope of the line passing though the points 126. Find the length of AB 127. Find the value of x. For questions 128 and 129, Simplify the following ratios, be sure to put the units on your answer. 128. 129. For questions 130 and 131, answer the questions using the diagram below given that 130. 131. . For questions 132 - 144, choose the correct answer. _______ 132. Find the a. b. _______ 133. If c. d. , what type of angle is a. acute _______ 134. . b. obtuse is the midpoint of a. 19 c. right d. straight 25 d. 50 Find the value of x. b. 43 c. _______ 135. What are the coordinates of the midpoint of the segment joining a. b. c. _______ 136. What is the measure of the supplement of a a. b. ? d. angle? c. d. _______ 137. Describe the slope of the line passing through the points a. Positive b. Negative c. Zero d. Undefined b. c. d. _______ 138. What is the a. _______ 139. Use the diagram to name a pair of alternate interior angles. a. b. c. d. _______ 140. What is the measure of a. b. c. d. _______ 141. What type of triangle is ? a. acute isosceles b. right scalene c. right isosceles d. obtuse scalene _______ 142. Identify the converse of the following statement: If an angle measures , then it is a straight angle. a. If an angle is a straight angle, then it measures b. If an angle doesn’t measure . , then it is not a straight angle. c. If an angle is not a straight angle, then it does not measure d. If an angle doesn’t measure _______ 143. What is measure of a. b. c. d. _______ 144. Find the value of x. a. 4 b. 5.6 c. 8 d. 8.2 , then it’s not a straight angle. . For questions 145 - 154, use the following as the reasons in your proof. You may use a reason more than once. Please write the letter of the reason in the blank. A. Vertical angles are congruent B. Transitive property of congruent angles C. Definition of right triangle D. All right angles are congruent E. Reflexive property of congruent segments F. SAS G. ASA I. Definition of segment bisector H. If two lines are perpendicular, then they form four right angles. J. HL K. If parallel lines are cut by a transversal, then alternate interior angles are congruent. L. A midpoint divides a segment into two congruent parts Given: Prove: Statement: Reason: Given 145. 145. _________________________________________ 146. 146. _________________________________________ 147. 147. _________________________________________ Given: B is the midpoint of Prove: Statement: Reason: Given B is the midpoint of 148. 148. _________________________________________ 149. 149. _________________________________________ 150. 150. _________________________________________ Given: is the perpendicular bisector of Prove: Statement: Reason: is the perpendicular bisector of Given 151. are right angles 151. _________________________________________ 152. are right triangles 152. _________________________________________ 153. 153. _________________________________________ 154. 154. _________________________________________ Geometry 235 Semester 1 Final – Answer Page Name: Date: 1. 25. 48. Comp: 71. 2. 26. Supp: 72. 3. 27. 49. 73. 4. 28. 50. 74. 5. 29. 51. 75. 6. 30. 52. 76. 7. 31. 53. 77. 8. 32. 54. 78. Angles 9. 33. 55. 10. 34. 56. 11. 35. 57. 12. 36. 58. 80. 13. 37. 59. 81. 14. 38. 60. 82. 15. 39. 61. 83. 16. 40. 62. 84. 17. 41. 63. 85. 18. 42. 64. 86. 19. 43. 65. 87. 20. 44. 66. 88. 21. 45. 67. 89. 22. 46. 68. 90. 23. 47. Comp: 69. 91. 24. Supp: 70. 92. Sides 79. Angles Sides 93. 119. 145. 94. 120. 146. 95. 121. 147. 96. 122. 148. 97. 123. 149. 98. 124. 150. 99. 125. 151. 100. 126. 152. 101. 127. 153. 102. 128. 154. 103. 129. 104. 130. 105. 131. 106. 132. 107. 133. 108. 134. 109. 135. 110. 136. 111. 137. 112. 138. 113. 139. 114. 140. 115. 141. 116. 142. 117. 143. 118. 144.