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Transcript 
Angles Formed by Parallel Lines and
3-2 Transversals
LESSON
Lesson Objectives (p. 155):
______________________________________________________________
______________________________________________________________
Key Concepts
1. Postulate 3-2-1—Corresponding Angles Postulate (p. 155):
THEOREM
HYPOTHESIS
CONCLUSION
2. Theorems—Parallel Lines and Angle Pairs (p. 156):
THEOREM
HYPOTHESIS
CONCLUSION
3-2-2 Alternate Interior Angles
Theorem
3-2-3 Alternate Exterior Angles
Theorem
3-2-4 Same-Side Interior
Angles Theorem
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
55
Geometry
Angles Formed by Parallel Lines and
3-2 Transversals
LESSON
Lesson Objectives (p. 155):
prove and use theorems about angles formed by parallel lines and a
______________________________________________________________
transversal.
______________________________________________________________
Key Concepts
1. Postulate 3-2-1—Corresponding Angles Postulate (p. 155):
THEOREM
If two parallel lines
are cut by a
transversal, then the
pairs of
corresponding angles
are congruent.
HYPOTHESIS
1
5
3 4
2
7
6
p
CONCLUSION
1
2
5
6
t
8
3
4
7
8
q
2. Theorems—Parallel Lines and Angle Pairs (p. 156):
THEOREM
HYPOTHESIS
1 3
2 4
3-2-2 Alternate Interior Angles
Theorem
If two parallel lines are cut
by a transversal, then the
pairs of alternate interior
angles are congruent.
1
4
3-2-3 Alternate Exterior Angles
Theorem
If two parallel lines are cut
by a transversal, then the
two pairs of alternate
exterior angles are
congruent.
2
3
5
8
3-2-4 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.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
CONCLUSION
6
5 7
6 8
7
m1 m4 180°
m2 m3 180°
1
4
55
2
3
Geometry
LESSON 3-2 CONTINUED
3. Get Organized Complete the graphic organizer by explaining why each of
the three theorems is true. (p. 157).
1
3
2
5
4
Corr. ⭄ Post.
Alt. Int. ⭄ Thm.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Alt. Ext. ⭄ Thm.
56
Same–Side Int. ⭄ Thm.
Geometry
LESSON 3-2 CONTINUED
3. Get Organized Complete the graphic organizer by explaining why each of
the three theorems is true. (p. 157).
1
3
2
5
4
Corr. ⭄ Post.
Alt. Int. ⭄ Thm.
Alt. Ext. ⭄ Thm.
Same–Side Int. ⭄ Thm.
⬔1 and ⬔3 are vert. ⭄, so ⬔1 ≅ ⬔3.
⬔2 and ⬔4 are vert. ⭄, so ⬔2 ≅ ⬔4.
⬔1 and ⬔5 form a lin. pair, so m⬔1
⬔1 and ⬔2 are corr. ⭄, so ⬔1 ≅ ⬔2.
⬔1 and ⬔2 are corr. ⭄, so ⬔1 ≅ ⬔2.
+ m⬔5 = 180°. ⬔1 and ⬔2 are corr.
⬔2 ≅ ⬔3 by Trans. Prop. of ≅
⬔1 ≅ ⬔4 by Trans. Prop. of ≅
⭄, so m⬔1 = m⬔2. m⬔2 + m⬔5 =
180° by subst. m⬔2 and m⬔5 are
supp. ⭄ by def. of supp. ⭄
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
56
Geometry
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