Parallel Lines Cut by a Transversal

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Parallel Lines Cut by a Transversal
J Pavlicek (2005) Edited by Judy Stoops (2007)
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Objectives

• Prove and use results about parallel lines and
  transversals

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Corresponding Angle Postulate If two parallel
lines are cut by a transversal, then
corresponding angles are congruent.
l
1
m
2
Given l m Prove 1 2
4
l
1
3
m
2
Given l m Prove ? 1 ? ? 3
Alternate Interior Angle Theorem If two parallel
lines are cut by a transversal, then alternate
interior angles are congruent.
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l
1
2
3
m
Given l m Prove ? 1 and ? 2 are
supplementary
Same-Side Interior Angle Theorem If two
parallel lines are cut by a transversal, then
same-side interior angles are supplementary.
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l
2
1
m
3
Given l m Prove ? 2 ? ? 3
Alternate Exterior Angle Theorem If two
parallel lines are cut by a transversal, then
alternate exterior angles are congruent.
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t
l
m
l
t
Given - Prove -
m
t
Perpendicular Transversal If a transversal is
perpendicular to one of two parallel lines, then
it is perpendicular to the other.
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Examples
1
2
4
3
5
6
8
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1) Name all the angles congruent to ?1.
2) Name all the angles supplementary to ?1.
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3) If m?4 110?, what is m?7?
4) If m?2 75?, what is m?8?
5) If m?5 (2x 5)? and m?3 (x 25)?, what
is the value of x and m?4?
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1
2
3
4
l
6
8
5
7
g h , m l
9
10
11
12
m
14
16
13
15
g
h
Circle, in red, all the angles congruent to ? 1.
Circle, in blue, all the angles congruent to ? 2.