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LESSON
3-2
Reading Strategies
Identify Relationships
The angles in this figure can be compared
using the following rules:
Corresponding
Angles Postulate
If two parallel lines are cut by
a transversal, then the pairs of
corresponding angles are
congruent.
Name the pairs of angles congruent
by the Corresponding Angles Postulate.
1. ___________________________
2. ___________________________
3. ___________________________
4. ___________________________
Alternate Interior
Angles Theorem
If two parallel lines are cut by
a transversal, then the two
pairs of alternate interior
angles are congruent.
Name the pairs of angles congruent
by the Alternate Interior Angles
Theorem.
5. ___________________________
6. ___________________________
Alternate Exterior
Angles Theorem
If two parallel lines are cut by
a transversal, then the two
pairs of alternate exterior
angles are congruent.
Name the pairs of angles congruent
by the Alternate Exterior Angles
Theorem.
7. ___________________________
8. ___________________________
Same-Side Interior
Angles Theorem
If two parallel lines are cut by
a transversal, then the two
pairs of same-side interior
angles are supplementary.
Name the pairs of angles
supplementary by the Same-Side
Interior Angles Theorem.
9. ___________________________
10. ___________________________
11. If m∠2 = 47°, then what is m∠6? How do you know?
_________________________________________________________________________________________
12. Based on the value for m∠6 from Exercise 11, what is m∠3? How do you know?
_________________________________________________________________________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
3-18
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.
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Holt McDougal Geometry