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LESSON 3.2 Answers for the lesson “Use Parallel Lines and Transversals” Skill Practice 11. Alternate Interior Angles Theorem 1. Sample: 12. Consecutive Interior Angles Theorem 1 2 13. Alternate Exterior Angles Theorem 14. Corresponding Angles Postulate 15. Alternate Exterior Angles 2. congruent: alternate interior Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. angles, alternate exterior angles, corresponding angles, vertical angles; supplementary: adjacent angles, consecutive interior angles, exterior angles on the same side of the transversal. 3. C 4. 658; Vertical Angles Congruence Theorem 5. 1108; Alternate Exterior Angles Theorem 6. 718; Alternate Interior Angles Theorem 7. 638; Consecutive Interior Angles Theorem 8. 548; Alternate Exterior Angles Theorem 16. Consecutive Interior Angles Theorem 17. m1 5 1508, m2 5 1508; Corresponding Angles Postulate, Vertical Angles Congruence Theorem 18. m1 5 1408, m2 5 408; Alternate Interior Angles Theorem, Consecutive Interior Angles Theorem 19. m1 5 1228, m2 5 588; Alternate Interior Angles Theorem, Consecutive Interior Angles Theorem 20. The lines are not known to be parallel, therefore 9 and 10 are not necessarily congruent. Theorem 9. Corresponding Angles Postulate 10. Alternate Interior Angles Theorem Geometry Answer Transparencies for Checking Homework 63 21. Sample answer: 1 > 4 by the 26. Sample answer: BAD and Alternate Exterior Angles Theorem; 1 > 2 >3 >4 by Vertical Angles Congruence Theorem, Alternate Interior Angles Theorem, and the Transitive Property of Angle Congruence. ABC, CDA and DCB 22. m1 5 1008, Consecutive Interior Angles Theorem; m2 5 808, Consecutive Interior Angles Theorem; m3 5 1008, Consecutive Interior Angles Theorem Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 23. m1 5 908, supplementary to the right angle by the Consecutive Interior Angles Theorem; m3 5 658, it forms a linear pair with the angle measuring 1158; m2 5 1158, supplementary to 3 by the Consecutive Interior Angles Theorem 24. m3 5 478, supplementary to the 27. 45, 85 28. 45, 20 29. 65, 60 30. 20, 10 31. 13, 12 32. 10, 25 33. B 34. M P Q N M and Q, P and N. Sample answer: P is supplementary to M and Q, therefore by the Congruent Supplements Theorem they are congruent; Q is supplementary to P and N, therefore by the Congruent Supplements Theorem they are congruent. 35. 65, 10 36. 8, 10 angle measuring 1338 by the Consecutive Interior Angles Theorem; m2 5 1338, it forms a linear pair with 3; m1 5 478, m1 5 m3 by the Alternate Interior Angles Theorem 25. Sample answer:BAC and DCA, ABD and CDB Geometry Answer Transparencies for Checking Homework 64 Problem Solving 41. Statements (Reason) 1. n i p 37. Statements (Reason) 1. p i q 2. 1 > 3 (Given) (Corresponding Angles Postulate) 3. 3 > 2 (Vertical Angles Congruence Theorem) 4. 1 > 2 (Transitive Property of Angle Congruence) 38. a. 4, 5, 8 b. 708 39. a. yes; 1 and 5, 2 and 6; Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. yes; 1 and 2, 1 and 6, 2 and 5, 5 and 6 b. Sample answer: The transversal stays parallel to the floor. 40. a. 708, 1108 b. Sample answer: 1 and 2 are corresponding angles and therefore congruent. 1 and 3 are supplementary so by substitution 2 and 3 are supplementary, so ABC is a straight angle. c. Yes; steeper. Sample answer: The points are collinear, if m1 is 608, the angle is smaller and the line becomes steeper. 2. 1 > 3 (Given) (Alternate Interior Angles Theorem) 3. m1 5 m3 (Definition of congruent angles) 4. 3 and 2 are supplementary. (Linear Pair Postulate) 5. m2 1 m3 5 1808 (Def. of supplementary angles) 6. m1 1 m2 5 1808 (Substitution Property) 7. 1 and 2 are supplementary. (Def. of supplementary angles) 42. Statements (Reason) 1. t > r; r i s (Given) 2. 1 is a right angle. (Def. of perpendicular lines) 3. m1 5 908 4. 1 > 2 (Definition of right angle) (Corresponding Angles Postulate) 5. m1 5 m2 (Definition of congruent angles) 6. m2 5 908 (Substitution) 7. 2 is a right angle. (Definition of right angle) 8. t > s (Definition of perpendicular lines) Geometry Answer Transparencies for Checking Homework 65 43. 608. Sample answer: 4 > 2 Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. by the Alternate Interior Angles Theorem, 2 > 3 by definition of angle bisector, 5 > 1 by Corresponding Angles Postulate, 4 > 5 is given, so 1 > 2 > 3 > 4 > 5. Since m1 1 m2 1 m3 5 1808, they must each be 608. Geometry Answer Transparencies for Checking Homework 66