Title: Parallel Lines Cut by a Transversal
1Parallel Lines Cut by a Transversal
J Pavlicek (2005) Edited by Judy Stoops (2007)
2Objectives
- Prove and use results about parallel lines and
transversals
3Corresponding 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
4l
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.
5l
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.
6l
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.
7t
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.
8Examples
1
2
4
3
5
6
8
7
1) Name all the angles congruent to ?1.
2) Name all the angles supplementary to ?1.
93) 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?
101
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.