Alternate exterior angles are two angles that are on the exterior of l and m, but on opposite sides of the transversal. Converse of the Alternate Exterior Angles Theorem: If two lines are cut ...Alternate exterior angles are two angles that are on the exterior of l and m, but on opposite sides of the transversal. Converse of the Alternate Exterior Angles Theorem: If two lines are cut by a transversal and the alternate exterior angles are congruent, then the lines are parallel. Alternate exterior angles are two angles that are on the exterior of two different lines, but on the opposite sides of the transversal.