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 *k* ||* l*, then

1 * *7

and

4 * *6.

**Proof.**

Since *l *|| *k*, by the Corresponding Angles Postulate,

1 5.

Also, by the Vertical Angles Theorem,

5 * *7.

Then, by the Transitive Property of Congruence,

1 7.

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* k* ||* l*.