So, in the figure below, if k || l, then
Since l || k, by the Corresponding Angles Postulate,
Also, by the Vertical Angles Theorem,
Then, by the Transitive Property of Congruence,
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.