Test 8 Chapter 2 Test Answers 1. (See question) (3) Directions: Write answers in the spaces provided. 2. (See question) (3) For each conditional, underline the hypothesis once and the conclusion twice. 3 (See question) (3) 1. If Michele plays her viola, then she must put rosin on her bow. 2. Class rank will be determined only if final exams are completed- 3, 3x + 1 = 1 implies x = 0. (3) Write the letter of the converse of each conditional (3) 4. If you go, then I stay. (A) If I go, then you stay. 5. I go if you stay. (BB) If you stay, then I go. (3) 6. I go only if you stay. (C) If I stay. then you go. (3) (D) If you go, then 1 stay. 10 (3) Classify each statement as true or false. 11. 7. Definitions may be used as reasons in a proof. 12. (31 8. A statement in the form If p and 4, then r is a biconditional. 13. 9. The converse of a true conditional is always true. 10. The converse of a false conditional is always false. 14. 11. Perpendicular lines form congruent adjacent angles 15. [See question) (3) 12. Two angles complementary to the same angle are complementary to 16. (See question; each other. 17. 13. Two angles congruent to the same angle are congruent to each other. 18 14. The Substitution Property and the Transitive Property may always 19 be used interchangeably 20, Draw a counterexample to show that each statement is false. 15. Vertical angles are never 16. Two lines always intersect. supplementary. In Questions 17-20. AD _ FC and m Z ! = 38. 17. m LADF = 1 18. m LEDC = 1 19. m / CDB = 1 20. m LADB = 2 Questions 17-20Test 8 (continued) Answers In Questions 21-23, Of 1 YS. Use the given 21. information to find the value of x. 21. 21. m LI = 3x; m (4 = x + 30 23. 131 22. m 43 = 2x + 20; m 24 = x + 10 23. m LI = x + 1; i Z V05 = 4x - 6 24. 431 R 24. If m _4 - y. then find the measure of 25. (31 L YOR in terms of ). Questions 21-24 26. 431 Write the letter of the reason that justifies each statement 17. (A) Definition of complementary (H) Definition of angle bisector angles 28 131 (B) Definition of supplementary (1) Angle Bisector Theorem angles 19. (C) Definition of perpendicular () Definition of right angle 30. lines (D) Angle Addition Postulate (K) Segment Addition Postulate 31. (E) If two lines are perpendicular. then they form congruent adjacent angles. 12. (See proof ) (F) If two lines form congruent adjacent angles. then the lines are perpendicular. (G) If the exterior sides of two adjacent acute angles are perpendicular. then the angles are complementary 25. If FB _ AC. then & 7 is complementary to FBC CHALLENGE (Optionall 26. If m 2 6 - 90, then & & is a right: angle Given: LB is a comp of LA 27. If 1 8 is a right angle. then FR _ AC L C is a supp. of _ B. 28. If BE biNews & FED then 2 7= [ b LD is a supp of L C 29. PHIL .ABD + I L DBC = 180 LE is a comp. of LD. LF is a comp of LE 30. IF FB : AC. then L8 = LFBC L. G is a supp. of LF 31. If m LFBD + 7: 5 = 90. then 8 L. FBD is complementary to 4 5 Questions 25-31 Then LG= G 32. Write a two-column proof. ANSWER Given. KH bisects L GKJ. Prove: 29 = 2 10 10 L 12 Proof