Since p∥q, we can use the corresponding angles postulate to state the following
[tex]\angle2\cong\angle3[/tex]
Then, by the Vertical Angles Theorem
[tex]\angle1\cong\angle3[/tex]
Then, by the transitive property of congruence
[tex]\angle1\cong\angle2[/tex]
And this proves that alternate exterior angles are congruent.
