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