Alternate Exterior Angles Theorem
The Alternate Exterior Angles Theorem states that, when two parallel lines are cut by a transversal , the resulting alternate exterior angles are congruent .
So, in the figure below, if , then
and .
Proof.
Since , by the Corresponding Angles Postulate ,
.
Also, by the Vertical Angles Theorem,
.
Then, by the Transitive Property of Congruence,
.
You can prove that and are congruent using the same method.
The converse of this theorem is also true; that is, if two lines and are cut by a transversal so that the alternate exterior angles are congruent, then .