Geometry Chapter 3 Review Answers 1. 2. 3. 4. 5. 6. 7. Parallel Skew Perpendicular HF, AC, BD CD, GH, DB, HF GE, EF, AC, AB Parallel lines are coplanar, but skew lines are not coplanar. 8. Parallel lines never intersect, skew lines never intersect. 9. Corresponding Angle Converse, Alternate Interior Angle Converse Alternate Exterior Angle Converse Consecutive Interior Angle Converse Transitive Property of Parallel Lines If 2 lines are perpendicular to the same line, they are parallel to each other. (p 192) 10. Yes; alternate interior angle converse 11. Yes; corresponding angle converse 12. Yes; consecutive interior angle converse 13. Yes; alternate exterior angle converse 14. Yes; Lines Perpendicular to a Transversal Th. “if 2 lines are perpendicular to the same line, they are parallel to each other.” (p192) 15. Yes; Transitive Property of Parallel Lines: If k // l and l // m, then k // m. 16. c // d; alternate exterior angle converse 17. a // b; consecutive interior angle converse 18. none; no angle relationship 19. a//b; corresponding angle converse 20. none; consecutive interior angles 180°. 21. c // d, m 6 = 70° (Vertical Angles) and m 4 + m 6 = 180° so lines are parallel by consecutive interior angle converse. 22. none; not enough information 23. c // d; m 7 = 75° (or m<6 = 75°) because linear pairs are supplementary. Lines are parallel by alternate exterior angle converse (or corresponding angle converse) 24. Both slopes are 4 so lines are parallel. 25. m = 2 3 , m = , so lines are . 2 3 4 3 , m = , so lines are neither. 3 4 4 5 //m = ; m = 5 4 1 m = ; //m = -2 2 1 m = 5; //m = 5 //m = undefined; m = zero 26. m = 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. x = 29 x = 5, y = 140 a = 74, n = 13 x = 20, w = 104 x = 4, y = 43 not // because the vertical angle of 130° is consecutive interior with 55°, but 130° + 55° 180° 37. Yes; Vertical angles are congruent and consecutive interior angle converse proves lines are parallel (also could have used corresponding angles) 38. not //; vertical angles are congruent, so (4x – 9) = (6x – 21) and x is 6. But then corresponding angles would not be =, so lines are not //. 39. Yes; because of a linear pair, we know (3x + 7) + (5x + 5) = 180° and x = 21. By corresponding angle converse, lines are parallel. 40. Yes; by consecutive interior angle theorem, 180° - 45° = 135° , so by alternate interior angle converse, m // k. 41. No; consecutive interior angles tell us that the alternate interior angle of 112° is 102°, but since they are not equal, the lines are not parallel. 42. 60° (Use Alternate Interior Angles) 43. 95° 44. 3 = 72°, 180° - (58° + 50°) = 72° 4 = 58°, alternate interior angles 5 = 50°, alternate interior angles/vertical angles