Corresponding Angles Theorem

It is given that l_1 and l_2 are parallel lines. Therefore, by the definition of parallel lines, there is a translation that maps one line onto another. It should be noted that when translating one line onto another, the pairs of corresponding angles overlap and seem to have the same measures. In fact, because a translation is a rigid motion, and a rigid motion preserves length and angle measures, the pairs of corresponding angles are congruent angles.