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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
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Find each angle measure.
4. m∠HJK
3. m∠1
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5. m∠ABC
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6. m∠MPQ
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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
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9. m∠RST
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10. m∠MNP
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11. m∠WXZ
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12. m∠ABC
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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
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A23
Holt McDougal Geometry