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Name ________________________________________ Date __________________ Class__________________ LESSON 3-1 Reteach Lines and Angles Lines Description Examples parallel lines that lie in the same plane and do not intersect symbol: || perpendicular lines that form 90° angles symbol: ⊥ skew lines that do not lie in the same plane and do not intersect A || m k and m are skew. k⊥ A Parallel planes are planes that do not intersect. For example, the top and bottom of a cube represent parallel planes. Use the figure for Exercises 1–3. Identify each of the following. 1. a pair of parallel lines _________________________________________ 2. a pair of skew lines _________________________________________ 3. a pair of perpendicular lines _________________________________________ Use the figure f or Exercises 4–9. Identify each of the following. 5. a segment that is perpendicular to GH 4. a segment that is parallel to DG _________________________________________ _________________________________________ 6. a segment that is skew to JF 7. one pair of parallel planes _________________________________________ _________________________________________ 8. one pair of perpendicular segments, not including GH 9. one pair of skew segments, not including JF _________________________________________ _________________________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 3-6 Holt McDougal Geometry Name ________________________________________ Date __________________ Class__________________ LESSON 3-1 Reteach Lines and Angles continued A transversal is a line that intersects two lines in a plane at different points. Eight angles are formed. Line t is a transversal of lines a and b. Angle Pairs Formed by a Transversal Angles Description Examples corresponding angles that lie on the same side of the transversal and on the same sides of the other two lines alternate interior angles that lie on opposite sides of the transversal, between the other two lines alternate exterior angles that lie on opposite sides of the transversal, outside the other two lines same-side interior angles that lie on the same side of the transversal, between the other two lines; also called consecutive interior angles Use the figure for Exercises 10–13. Give an example of each type of angle pair. 10. corresponding angles 11. alternate exterior angles _________________________________________ 12. same-side interior angles _________________________________________ 13. alternate interior angles _________________________________________ _________________________________________ Use the figure for Exercises 14–16. Identify the transversal and classify each angle pair. 14. ∠1 and ∠2 _________________________________________ 15. ∠2 and ∠4 16. ∠3 and ∠4 _________________________________________ _________________________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 3-7 Holt McDougal Geometry Answers for the chapter Parallel and Perpendicular Lines Practice C 3-1 LINES AND ANGLES 1. Practice A 1. Skew 2. intersect 3. 90° or right 4. Parallel 5. AC & EG Lines j and A are parallel. 6. AC and Dh are skew. 2. 7. CG ⊥ EG 8. plane ABD || plane EFH 9. lines 10. Corresponding 11. outside 12. Alternate 13 same 14. line r Lines j and A are skew. 3. 15. ∠1 and ∠3 or ∠2 and ∠4 16. ∠2 and ∠3 17. ∠1 and ∠4 Practice B Lines j and A are perpendicular. 1. BE & AD 4. 2. AB and CF are skew. 3. CF ⊥ EF 4. plane ABC || plane DEF 5. line z Lines j and A are parallel. 6. lines x and y 7. Sample answer: ∠1 and ∠3 5. X = 10; O = 10 8. Sample answer: ∠2 and ∠6 6. X = 40; O = 70 7. 9. Sample answer: ∠1 and ∠5 10. Sample answer: ∠2 and ∠3 11. transv.: utility pole; same-side interior angles 8. 12. transv.: tension wire; alternate exterior angles 13. transv.: telephone line; corresponding angles 14. transv.: utility pole; alternate interior angles Reteach 1. g || h 2. j and h 3. j ⊥ g 4. Possible answers: EH or FJ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. A21 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