What are alternate exterior angles?

How to find this angle pair

When the lines are parallel, alternate exterior angles are congruent. That fact mirrors the alternate interior rule, except that the chosen pair sits beyond the outer sides of the two lines instead of between them.

The positional name still makes sense in a non-parallel setup, but the equal-measure result depends on the lines being parallel. Keeping those two ideas separate is important for accurate reasoning.

To find the pair, first mark the regions outside the two lines. Then compare the sides of the transversal. One angle should sit on one side at one crossing, and the other should sit on the opposite side at the other crossing.

With parallel lines, alternate exterior angles have equal measures. A pair can have the right positions even when the lines are not parallel, but the theorem about equality belongs only to the parallel case.

• Alternate exterior angles lie outside the lines on opposite sides of the transversal.
• Exterior means the angles lie outside the two crossed lines.
• Alternate means the pair sits on opposite sides of the transversal.
• With parallel lines, alternate exterior angles have equal measure.

Where alternate exterior angles help

• Use alternate exterior angles in parallel-line angle proofs and missing-measure questions.
• Use them when checking outside angle positions created by one transversal.
• Use them to justify equal angles in diagrams where the chosen pair is not between the lines.

Three alternate-exterior checks

• Do not pick a pair between the lines and still call it exterior.
• Do not choose two outside angles on the same side of the transversal; that is a different relationship.
• Do not claim equality without the parallel-line condition that makes the theorem valid.