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Name ________________________________________ Date __________________ Class__________________ LESSON 3-2 Reteach Angles Formed by Parallel Lines and Transversals According to the Corresponding Angles Postulate, if two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Determine whether each pair of angles is congruent according to the Corresponding Angles Postulate. 2. ∠3 and ∠4 1. ∠1 and ∠2 _________________________________________ ________________________________________ Find each angle measure. 4. m∠HJK 3. m∠1 _________________________________________ 5. m∠ABC ________________________________________ 6. m∠MPQ _________________________________________ ________________________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 3-14 Holt McDougal Geometry Name ________________________________________ Date __________________ Class__________________ LESSON 3-2 Reteach Angles Formed by Parallel Lines and Transversals continued If two parallel lines are cut by a transversal, then the following pairs of angles are also congruent. Angle Pairs Hypothesis Conclusion alternate interior angles ∠2 ≅ ∠3 ∠6 ≅ ∠7 alternate exterior angles ∠1 ≅ ∠4 ∠5 ≅ ∠8 If two parallel lines are cut by a transversal, then the pairs of same-side interior angles are supplementary. m∠5 + m∠6 = 180° m∠1 + m∠2 = 180° Find each angle measure. 7. m∠3 8. m∠4 _________________________________________ 9. m∠RST _________________________________________ 10. m∠MNP _________________________________________ 11. m∠WXZ _________________________________________ 12. m∠ABC _________________________________________ _________________________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 3-15 Holt McDougal Geometry 3. m∠1 + m∠4 + m∠ABE + m∠DEB = 360° 3. Add. Prop. of = 7. ∠1 ≅ ∠7 8. ∠4 ≅ ∠6 9. m∠2 + m∠5 = 180° 4. m∠3 + m∠CEB + m∠CBE = 180° 4. Given 10. m∠3 + m∠8 = 180° 5. m∠DEB + m∠CEB = 180° 5. Lin. Pair Thm. 6. m∠3 + m∠CEB + m∠CBE = m∠DEB + m∠CEB 6. Subst. (Steps 4, 5) 11. m∠6 = 47° by the Corresponding Angles Postulate 7. m∠3 + m∠CBE = m∠DEB 8. m∠1 + m∠3 + m∠4 + m∠ABE + m∠CBE = 360° 9. m∠2 = m∠ABE + m∠CBE 10. m∠1 + m∠2 + m∠3 + m∠4 = 360° 12. m∠3 = 133° by the Same-Side Interior Angles Theorem 7. Subtr. Prop. of = 8. Subst. (Steps 3, 7) 3-3 PROVING LINES PARALLEL Practice A 9. Angle Add. Post. 10. Subst. (Steps 8, 9) 1. parallel 2. Conv. of Corr. ∠s Post. 3. m∠7 = 68°, ∠3 ≅ ∠7, Conv. of Corr. ∠s Post. Reteach 1. no 2. yes 4. transversal; congruent 3. 67° 4. 142° 5. supplementary 5. 92° 6. 125° 7. 7. 111° 8. 90° 9. 138° 10. 56° 11. 130° 12. 118° 6. parallel Statements 1. ∠1 and ∠3 are supplementary. Challenge 1. Justifications may vary. All lines directed due north are parallel. A heading that is read off the compass is the same as the ship’s heading. 2. about 102° 3. about 38° 4. about 170° 5. about 256° Reasons 1. a. Given 2. b. ∠2 and ∠3 are supplementary. 2. Linear Pair Thm. 3. ∠1 ≅ ∠2 3. c. ≅ Supps. Thm. 4. d. m || n 4. Conv. of Corr. ∠s Post. Practice B 1. m || n; Conv. of Alt. Int. ∠s Thm. 2. m || n; Conv. of Corr. ∠s Post. Problem Solving 1. 17; Alt. Int. ∠s Thm. 3. m and n are parallel if and only if m∠7 = 90°. 2. 102°; Alt. Ext. ∠s Thm. 3. x = 10; y = 3; (12x + 2y)° = 126° by the Corr. ∠s Post. and (3x + 2y)° = 36° by the Alt. Int. ∠s Thm. 4. D 5. H 4. m || n; Conv. of Same-Side Int. ∠s Thm. 5. m and n are not parallel. 6. m || n; Conv. of Corr. ∠s Post. 7. m || n; Conv. of Alt. Ext. ∠s Thm. Reading Strategies 8. m and n are not parallel. 1. ∠1 ≅ ∠5 2. ∠2 ≅ ∠6 3. ∠3 ≅ ∠7 4. ∠4 ≅ ∠8 5. ∠2 ≅ ∠8 6. ∠3 ≅ ∠5 9. Sample answer: The given information states that ∠1 and ∠3 are supplementary. ∠1 and ∠2 are also Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. A23 Holt McDougal Geometry