alternate exterior angles are congruent
if two parallel lines are cut by a transversal, then alternate interior angles are congruent
Alternate exterior angles are angles that are on opposite sides of the transversal and outside of the two parallel lines. When two parallel lines are intersected by a transversal, alternate exterior angles are congruent. In other words, the measure of one alternate exterior angle is equal to the measure of the other alternate exterior angle.
To prove this, suppose there are two parallel lines, line m and line n, that are intersected by a transversal line t. Let’s say that angle 1 and angle 2 are alternate exterior angles, which means they are on opposite sides of the transversal and both outside of the two parallel lines.
We know that line m and line n are parallel, so angle 1 and angle 2 are corresponding angles. Corresponding angles are congruent when two parallel lines are intersected by a transversal. Therefore, we know that angle 1 is congruent to angle 2.
Hence, we have proved that alternate exterior angles are congruent when two parallel lines are intersected by a transversal.
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