Proving that a Quadrilateral Is a Parallelogram GEOMETRY LESSON 6-3 Pages 307-310 Exercises 1. 5 2. x = 3, y = 4 3. x = 1.6, y =1 4. 5. 5 6. 13 7. Yes; both pairs of opp. sides are . 8. No; the quad. Could be kite. 9. Yes; both pairs of opp. are . 10. No; the quad. could be a trapezoid. 11. Yes; both pairs of opp. sides are because alt. int. are . 12. Yes; one pair of opp sides are and . 13. Yes; both pairs of opp. sides are . 14. No; opp. sides are not . 15. No; the quad. could be a kite. 16. It remains a because the shelves and connecting pieces remain . s 5 3 s 6-3

Proving that a Quadrilateral Is a Parallelogram GEOMETRY LESSON 6-3 17. a. bisect b. XR c. XYR d. ASA e. alt. interior 18. Opp. sides of a quad. are if and only if the quad. is a 19. a. Distr. Prop. b. Div. Prop. of Eq. c. AD BC, AB DC d. If same-side int. are suppl., the lines are . e. Def. of 20. Yes; both pairs of opp. are . 21. No; the figure could be a kite. 22. Yes; a pair of opp. sides is and . 23. No; the figure could be a trapezoid. 24. Yes; the both pairs of opp. sides are . 25. Yes; diag. bisect each other. 26. x = 15, y = 25 27. x = 3, y = 11 s s 6-3

Proving that a Quadrilateral Is a Parallelogram GEOMETRY LESSON 6-3 28. c = 8, a = 24 29. k = 9, m = 23.4 30. Answers may vary. Sample: 31. 32. (4, 0) 33. (6, 6) 34. (–2, 4) 35. You can show a quad. is a if both opp. sides are , if both opp. are , if opp. sides are , if diag. bisect each other, if all consecutive are suppl., if one pair of opp. sides are both and . 36. Answers vary. Sample: 1. TRS RTW (Given) 2. RS TW, SRT WTR (CPCTC) 3. SR WT (If alt. int. are , then lines are .) 1 6 s 6-3

Proving that a Quadrilateral Is a Parallelogram GEOMETRY LESSON 6-3 36. (continued) 4. RSTW is a . (If one pair of opp. sides are and , then it is a .) 37. Answers may vary. Sample: 1. AB CD, AC BD (Given) 2. ACDB is a . (If opp. sides are , then it is a .) 3. M is the midpoint of BC. (The diag. of a bisect each other.) 4. AM is a median. (Def. of a median) 38. G(–4, 1), H(1, 3) 39. C 40. F 41. C 42. H 6-3

Proving that a Quadrilateral Is a Parallelogram GEOMETRY LESSON 6-3 43. [2] Statements Reasons 1. NRJ CPT (Given) 2. NJ CT (CPCTC) 3. NJ TC (Given) 4. JNTC is a . (If opp. sides of a quad. are both and , then the quad. is a .) [1] proof missing steps 44. [4] a. 6x = 7x – 11; x = 11 b. Yes; m ABC = m CDE = 66 c. Yes; BD FE and BF DE [3] one or more error in calculating x [2] one explanation is incorrect [1] only part (a) answered 6-3

Proving that a Quadrilateral Is a Parallelogram GEOMETRY LESSON 6-3 45. a = 8, h = 30, k = 20 46. m = 9.5, x = 15 47. e = 17, f = 11, c = 204 48. It is given that AD BC and DAB CBA. By the Reflexive Prop. of AB AB, thus DAB CBA by SAS, so AC BD by CPCTC. 49. If a quad. is a , then the diag. bisect each other; if the diag. of a quad. bisect each other, then it is a . 50. If two lines and a transversal form corr. , then the two lines are ; if two lines are , then a transversal forms corr. . 51. If the prod. of the slopes of two nonvertical lines is –1, then they are ; if two nonvertical lines are , then the prod. of their slopes os –1. s s 6-3