Question

prove that if two parallel lines are crossed by a transversal, then alternate exterior angles are congruent

Answer 1

Since p∥q, we can use the corresponding angles postulate to state the following

$\angle2\cong\angle3$

Then, by the Vertical Angles Theorem

$\angle1\cong\angle3$

Then, by the transitive property of congruence

$\angle1\cong\angle2$

And this proves that alternate exterior angles are congruent.