Answers for 3.3 For use with pages

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1 Answers for Skill Practice. Sample: n m. no 3. yes; Corresponding Angles 4. no 5. yes; Alternate Exterior Angles 6. Sample answer: and 8, and 7. Given two lines cut by a transversal, alternate interior angles are congruent if and only if the lines are parallel; given two lines cut by a transversal, alternate exterior angles are congruent if and only if the lines are parallel; given two lines cut by a transversal, consecutive interior angles are supplementary if and only if the lines are parallel The student believes that x 5 y but there is no indication that they are equal. 0. yes; Alternate Interior Angles. yes; Alternate Exterior Angles m , Vertical Angles Congruence Theorem; m , Linear Pair Postulate; m 5 308, Vertical Angles Congruence Theorem; m , Alternate Interior Angles Theorem; m , Vertical Angles Congruence Theorem; m , Linear Pair Postulate; m , Vertical Angles Congruence Theorem A7

2 7. a. m DCG 5 58, m CGH b. They are consecutive interior angles and they are supplementary. c. yes; Consecutive Interior Angles 8. a. Sample: b. Given: and are supplementary, Prove: p i q 9. yes; Consecutive Interior Angles 0. yes; Alternate Exterior Angles. no. The student assumed the congruent angles were alternate interior angles between ] AD and ] BC. By the Alternate Interior Angles ; ] AB i ] DC. 3. D p q 4. angle. Sample answer: Using the Vertical Angles Congruence Theorem, the Linear Pair Postulate, and the Alternate Interior Angles Theorem the other angle measures can be found. 5. Sample answer: > 4 therefore 4 and 7 are supplementary. Lines j and k are parallel by the Consecutive Interior ] Angles. 6. EA i ] HC ; EB ] is not parallel to HD ], GHC > HEA, GHD is not congruent to HEB. 7. a. line b. an infinite number of lines c. plane 8. a. 54 b c. No, Sample answer: For p to be parallel to q, x 5 54, then y 5 63 because of the linear pair formed, but in order for r and s to be parallel, y must equal Problem Solving 9. Alternate Interior Angles Theorem 30. Corresponding Angles A8

3 3. 3. Substitution 4. Definition of supplementary angles 5. Consecutive Interior Angles 3. Alternate Exterior Angles Theorem 33. Yes. Sample answer: E 0th is parallel to E 9th by the Corresponding Angles Postulate. E 9th is parallel to E 8th by the Alternate Exterior Angles Theorem. E 8th is parallel to E 7th by the Alternate Interior Angles Theorem. They are all parallel by the Transitive Property of Parallel Lines. 34. Statements (Reasons). >, 3 > 4 (Given). > 3 (Vertical Angles Congruence Theorem) 3. > 4 (Transitive Property of Angle Congruence) 4. } AB i } CD (Alternate Interior Angles Theorem) 35. Statements (Reasons). a i b, > 3 (Given). and 4 are supplementary. (Consecutive Interior Angles Theorem) 3. 3 and 4 are supplementary. ( Substitution) 4. c i d (Consecutive Interior Angles Theorem) 36. Statements (Reasons). > 7 (Given). and 4 are supplementary. ( Linear Pair Postulate) 3. 7 > 6 (Vertical Angles Congruence Theorem) 4. 6 and 4 are supplementary. (Substitution) 5. m i n (Consecutive Interior Angles Postulate) 37. You are given that 3 and 5 are supplementary. By the Linear Pair Postulate, 5 and 6 are also supplementary. So 3 > 6 by the Congruent Supplements Theorem. By the Alternate Interior Angles Theorem, m i n. A9

4 38. a. p 3 q b. Given: p i q and q i r, Prove: p i r c. Statements (Reasons). p i q and q i r (Given). > (Alternate Interior Angles Theorem) 3. > 3 (Vertical Angles Congruence Theorem) 4. 3 > 4 (Alternate Interior Angles Theorem) 5. > 4 (Transitive Property of Angle Congruence) 6. p i r (Alternate Interior Angles Theorem) 39. a. Sample answer: Corresponding Angles Theorem b. Slide the triangle along a fixed horizontal line and use the edge that forms the 908 angle to draw vertical lines. 4 r t Sample answers are given. 40. Consecutive Interior Angles Theorem 4. Vertical Angles Congruence Theorem followed by the Consecutive Interior Angles Theorem 4. Corresponding Angles Postulate 43. Vertical Angles Congruence Theorem followed by the Corresponding Angles Postulate 44. Consecutive Interior Angles Theorem 45. a. A C P 3 4 b. Yes; if two parallel lines are cut by a transversal, the angle bisectors of alternate interior angle pairs are parallel. Q B D n A0

5 45. b. (cont.) Statements (Reasons). l i n (Given). AQP > BPQ ( Alternate Interior Angles Theorem) 3. m 5 m AQP, m m BPQ ( Angle Addition Postulate) 4. m 5 m, m 3 5 m 4 ( Definition of angle bisector) 5. m m 5 m AQP, m 3 m 3 5 m BPQ (Subtitution) 6. m 5 m 3 (Transitive Property of Equality) 7. m 5 m 3 (Division Property of Equality) 8. > 3 (Definition of Congruent Angles) ] 9. QC i PD ] (Alternate Interior Angles Theorem) 3.3 Mixed Review } } } sandwiches 5. 4; by the Transitive Property of Congruence, } AB > } CD, so 9x 5 6x, 3x 5, x } } Mixed Review of Problem Solving 54.. a. Sample answer: q and p, k and m b. Sample answer: q and m c. Sample answer: n and m, n and k. a. : supplementary, 3: supplementary, 4: vertical, 5: corresponding, 6: supplementary, 7: alternate exterior, 8: exterior b., 6, ; Alternate Exterior Angles Theorem 4. yes; Alternate Interior Angles Theorem 5. a. b. 38; Transitive Property of Parallel Lines and Alternate Interior Angles Theorem A

6 6. 508; , supplementary to 888; 68, c i d by the Alternate Interior Angles Theorem followed by the Consecutive Interior Angles Theorem. A