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Name ________________________________________ Date __________________ Class__________________ LESSON 3-2 Practice B Angles Formed by Parallel Lines and Transversals Find each angle measure. 1. m∠1 _______________________ 2. m∠2 _______________________ – + 3. m∠ABC _______________________ 4. m∠DEF _______________________ Complete the two-column proof to show that same-side exterior angles are supplementary. 1 5. Given: p || q Prove: m∠1 + m∠3 = 180° p 2 q 3 Proof: Statements Reasons 1. p || q 1. Given 2. a. _______________________ 2. Lin. Pair Thm. 3. ∠1 ≅ ∠2 3. b. _______________________ 4. c. _______________________ 4. Def. of ≅ ∠s 5. d. _______________________ 5. e. _______________________ 6. Ocean waves move in parallel lines toward the shore. The figure shows Sandy Beaches windsurfing across several waves. For this exercise, think of Sandy’s wake as a line. m∠1 = (2x + 2y)° and m∠2 = (2x + y)°. Find x and y. x = _________ y = _________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 3-12 Holt McDougal Geometry 3. All four segments are marked with the same arrows. 4. Sample answer: Parallel lines are coplanar lines that never intersect, and perpendicular lines intersect at 90° angles. 5. Sample answer: HJ 6. Sample answer: DE 7. plane DEF || plane GHJ 8. Sample answer: DE ⊥ EF 9. Sample answer: HE and DF 10. Sample answer: ∠1 and ∠3 11. Sample answer: ∠1 and ∠8 12. Sample answer: ∠2 and ∠3 13. Sample answer: ∠2 and ∠7 14.transv. n; same-side int. ∠s 15. transv. m; alt. ext. ∠s 16. transv. p; corr. ∠s 3-2 ANGLES FORMED BY PARALLEL LINES AND TRANSVERSALS Practice A 2. no; yes 3. PR + RQ = PQ 4. The distance PR + RQ, the length of the path from P to Q traveling in a counterclockwise direction, is much longer than the length of the path traveling from P to Q in a clockwise direction. So, PR + RQ ≠ PQ. 5. Any two lines will intersect at exactly two points. 6. If the two points are at opposite “poles,” then infinitely many lines will pass through them. Problem Solving 1. Sample answer: No; AP is skew to RS and RS is skew to AD , but AP is not skew to AD . 3. 4. 5. 7. 5. 75 6. 150 9. congruent 11. ∠1 and ∠7; ∠2 and ∠8 12. ∠3 and ∠6; ∠4 and ∠5 Practice B 1. 47° 3. 97° 2. 119° 4. 62° 5. Statements Reasons 1. p �� q 1. Given 2. a. m∠2 + m∠3 = 180° 2. Lin. Pair Thm. 3. ∠1 ≅ ∠2 3. b. Corr. ∠s Post. 4. c. m∠1 = m∠2 4. Def. of ≅ ∠s 5. d. m∠1 + m∠3 = 180° 5. e. Subst. 6. 15; 40 Practice C 1. Sample answer: m∠1 + m∠2 = 180° and m∠3 + m∠4 = 180° by the Same-Side Int. ∠s Thm. Thus, the total of the angle measures is 360°. 2. 360° Reading Strategies 2. Yes, there is a right angle box at their intersection. 4. 70° 10. ∠3 and ∠5; ∠4 and ∠6 CF Sample answer: ∠DEB and ∠CBE B parallel lines 6. J skew A 1. LP and MQ 3. 140° 8. supplementary 2. Sample answer: No; PQ is skew to AD but not to PS . 2. equal 7. parallel; transversal Challenge 1. no; no 1. congruent 3. 360°; sample answer: Statements Reasons HJJG 1. Draw BE parallel to AD. 1. Construction 2. m∠1 + m∠ABE = 180°, m∠4 + m∠DEB = 180° 2. Same-Side Int. ∠s Thm. Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. A22 Holt McDougal Geometry