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.