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3-14 Holt Geometry

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.

1. ∠1 and ∠2 2. ∠3 and ∠4

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Find each angle measure.

3. m∠1 4. m∠HJK

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5. m∠ABC 6. m∠MPQ

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LESSON

3-2

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3-15 Holt Geometry

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. If two parallel lines are cut by a transversal, then the pairs of same-side interior angles are supplementary.

Find each angle measure.

7. m∠3 8. m∠4

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9. m∠RST 10. m∠MNP

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11. m∠WXZ 12. m∠ABC

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LESSON

3-2

Angle Pairs Hypothesis Conclusion

alternate interior angles

∠2 ≅ ∠3 ∠6 ≅ ∠7

alternate exterior angles

∠1 ≅ ∠4 ∠5 ≅ ∠8

m∠5 + m∠6 = 180° m∠1 + m∠2 = 180°

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A22 Holt Geometry

9. m∠2 = m∠ABE + m∠CBE 9. Angle Add. Post.

10. m∠1 + m∠2 + m∠3 + m∠4 = 360°

10. Subst. (Steps 8, 9)

Reteach 1. no 2. yes 3. 67° 4. 142° 5. 92° 6. 125° 7. 111° 8. 90° 9. 138° 10. 56° 11. 130° 12. 118°

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°

Problem Solving 1. 17; Alt. Int. s∠ Thm. 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

Reading Strategies 1. ∠1 ≅ ∠5 2. ∠2 ≅ ∠6 3. ∠3 ≅ ∠7 4. ∠4 ≅ ∠8 5. ∠2 ≅ ∠8 6. ∠3 ≅ ∠5 7. ∠1 ≅ ∠7 8. ∠4 ≅ ∠6 9. m∠2 + m∠5 = 180° 10. m∠3 + m∠8 = 180° 11. m∠6 = 47° by the Corresponding Angles

Postulate 12. m∠3 = 133° by the Same-Side Interior

Angles Theorem

LESSON 3-3

Practice A 1. parallel

2. Conv. of Corr. s∠ Post. 3. m∠7 = 68°, ∠3 ≅ ∠7, Conv. of Corr. s∠

Post. 4. transversal; congruent 5. supplementary 6. parallel 7.

Statements Reasons

1. ∠1 and ∠3 are supplementary.

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. 3. m and n are parallel if and only if

m∠7 = 90°. 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. 8. m and n are not parallel. 9. Sample answer: The given information

states that ∠1 and ∠3 are supplementary. ∠1 and ∠2 are also supplementary by the Linear Pair Theorem. Therefore ∠3 and ∠2 must be congruent by the Congruent Supplements Theorem. Since ∠3 and ∠2 are congruent, HI and JK are parallel by the Converse of the Corresponding Angles Postulate.

Practice C 1. x = 11; y = −5; m∠1 = 57°; m∠2 = 57°;

m∠3 = 123°

2.