3.3 Proving Lines are Parallel
In the previous section we used the fact that two lines were parallel to determine
congruent angle pairs. In this section we use the converse of those theorems. We will
use congruent pairs of angles to determine if two lines are parallel.
Corresponding Angles Converse:
If two lines are cut by a transversal and corresponding angles are congruent, then
the lines are parallel
Alternate Interior Angles Converse:
If two lines are cut by a transversal and alternate interior angles are congruent,
then the lines are parallel.
Alternate Exterior Angles Converse:
If two lines are cut by a transversal and alternate interior angles are congruent,
then the lines are parallel.
Same-Side Interior Angles Converse:
If two lines are cut by a transversal and consecutive interior angles are
supplementary, then the lines are parallel.
Transitive Property of Parallel Lines:
If two lines are parallel to the same line, then they are parallel to each other.
Ex: Given that m !1 " m ! 9
what can you conclude?
l
A 9
Ex: Given m !11" m !14
what can you conclude?
11
B 13
Ex: Given m ! 3 " m ! 8
what can you conclude?
Ex: Given m !15 " m ! 9
what can you conclude?
16
1
10
12
3
5
14
15
H
F
G
6
E
D
4
8
7
2
C
Ex:
Solve for x so that m || n.
Ex: Determine if there is enough information to prove p || q.