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Math 20-2 Chapter 2 Properties of Angles and Triangles Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which pairs of angles are equal in this diagram? a. b. c. d. b = c, e = g, and f = h b = f, c = g, and d = h b = e, c = h, and d = g b = a, c = e, and d = f 2. In which diagram(s) is AB parallel to CD? 1. a. b. c. d. 2. Choice 1 only Choice 2 only Choice 1 and Choice 2 Neither Choice 1 nor Choice 2 3. Which statement about the angles in this diagram is false? a. b. c. d. e = 130° f = 62° c = 50° b = 50° 4. Which angle property proves DAB = 120°? a. b. c. d. alternate exterior angles corresponding angles vertically opposite angles alternate interior angles 5. Which angle property proves EFS = 28°? a. alternate exterior angles b. supplementary angles c. alternate interior angles d. corresponding angles 6. Which are the correct measures of the indicated angles? a. b. c. d. w = 77°, x =103°, y = 103° w = 77°, x =77°, y = 103° w = 103°, x =103°, y = 77° w = 103°, x =77°, y = 77° 7. Which are the correct measures for DCE and CAB? a. DCE = 31°, CAB = 134° b. DCE = 47°, CAB = 109° c. DCE = 13°, CAB = 143° d. DCE = 37°, CAB = 119° 8. Which are the correct measures for OJK, JKO, and JOK? 11. With which of the following polygons could you create a tiling pattern? Choose the best answer. a. b. c. d. a square an equilateral triangle a rectangle all of the above 12. With which of the following polygons could you create a tiling pattern? a. b. c. d. OJK = 117°, JKO = 28°, and JOK = 35° OJK = 117°, JKO = 36°, and JOK = 37° OJK = 152°, JKO = 18°, and JOK = 10° OJK = 102°, JKO = 28°, and JOK = 50° 9. Which are the correct measures of the interior angles of CDE? a. b. c. d. a regular octagon a regular pentagon a regular hexagon none of the above 13. The sum of the measures of the interior angles of a convex polygon is S. Which expression results in the number of sides of the polygons? a. b. 180°(S – 2) c. d. a. b. c. d. DCE = 48°, CDE = 75°, and CED = 57° DCE = 37°, CDE = 86°, and CED = 57° DCE = 57°, CDE = 86°, and CED = 37° DCE = 37°, CDE = 68°, and CED = 75° 14. Determine the value of c. 10. Determine the sum of the measures of the interior angles of this polygon. a. b. c. d. 1620° 1080° 1260° 1440° a. b. c. d. 45° 72° 54° 48° 15. State the corresponding sides and angles in this pair of congruent triangles. a. b. c. d. AB RS, AC RT, AR AB RT, AC RS, AT BC RS, AC ST, AS None of the above choices are correct. 16. What can you deduce from the statement ABC DFE? a. b. c. d. 118.What additional piece of information would allow you to conclude that these triangles are congruent? a. b. c. d. A = D and C = F B = E AC = DF all of the above 19. Which angle is equal to D? C = D B = D A = F none of the above 17. What additional piece of information would allow you to conclude that these triangles are congruent? a. b. c. d. A B C none of the above 20. Which angle is equal to F? a. b. c. d. AC = DF C = F AB = EF all of the above a. b. c. d. A B C none of the above Short Answer 21. Determine the measure of PQR. 23. Given QP || MR, determine the measure of MOQ. 24. Can you prove these triangles are congruent? If so, how? 22. Determine the measure of NMO. Problem 25. Prove that a triangle cannot contain two right angles. 26. Is quadrilateral MATH a parallelogram? Explain. 27. Determine the length of DE. Show your reasoning. Math 20-2 Chapter 2 Properties of Angles and Triangles - Answer Section MULTIPLE CHOICE 1. 5. 9. 13. 17. ANS: ANS: ANS: ANS: ANS: B A B A A 2.ANS B 6.ANS:D 10.ANS:A 14.ANS:C 18.ANS: D 3.ANS:D 7.ANS:D 11.ANS:D 15.ANS:A 19.ANS:B 4.ANS:C 8.ANS:A 12.ANS:C 16.ANS:D 20.ANS:C SHORT ANSWER 21. ANS: PQR = 122° 22. ANS: NMO = 82° 23. ANS: MOQ = 82° 24. ANS: Yes, by SSS. PROBLEM 25. ANS: For example, assume that ABC does contain two right angles, A, and B. A + B + C = 180° Sum of angles in triangle is 180° 90° + 90° + C = 180° Substitute known values. C = 180° – 90° – 90° Determine C. C = 0° This result is not possible, since C must be greater than 0°. Therefore, a triangle cannot contain two right angles. 26. ANS: It is not a parallelogram. AMT does not equal MTH, so alternate interior angles are not equal. KEY: angles| triangles 27. ANS: AB = BC A = DBC ABE = C ABE BCD BE = 10 BD = 15 DE = 5 Given sides Given angles Given angles ASA Corresponding sides with CD Corresponding sides with AE 15 – 10 = 5