Concept

Alternate Exterior Angles

Consider a pair of lines cut by a transversal. The pairs of exterior angles with different vertices that lie on opposite sides of the transversal are called alternate exterior angles.
Alternate exterior angles
In the diagram, two pairs of angles can be identified as alternate exterior angles.
If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent. The same logic in reverse can be applied. If two lines and a transversal form alternate exterior angles that are congruent, then the lines are parallel.
If Then
and
or

These statements are supported by the Alternate Exterior Angles Theorem and its converse.

Exercises