Alternate angles are angles that are in opposite positions relative to a transversal intersecting two lines.

If the alternate angles are between the two lines intersected by the transversal, they are called alternate interior angles.

In each illustration below, LINE 1 is a transversal of LINE 2 and LINE 3. In each illustration below, the following angles are alternate interior angles:

• A and G
• D and F

If the alternate angles are outside the two lines intersected by the transversal, they are called alternate exterior angles.

In each illustration below, LINE 1 is a transversal of LINE 2 and LINE 3. In each illustration below, the following angles are alternate exterior angles:

• B and H
• D and ∠E

When a transversal intersects two lines, the two lines are parallel if and only if alternate angles are congruent (equal in measure).

In illustration one of the example section above, LINE 1 and LINE 2 are parallel and alternate angles are congruent.

In illustration two of the example section above, LINE 1 and LINE 2 are NOT parallel and alternate angles are NOT congruent.