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 kl , then

17 and 46 .

Two parallel lines cut by a transversal n, with angles labeled 1 through 8

Proof.

Since kl , by the Corresponding Angles Postulate,

15 .

Also, by the Vertical Angles Theorem,

57 .

Then, by the Transitive Property of Congruence,

17 .

You can prove that 4 and 6 are congruent using the same method.

The converse of this theorem is also true; that is, if two lines k and l are cut by a transversal so that the alternate exterior angles are congruent, then kl .