Given ab is parallel to dc prove triangle abe is congruent to triangle dce

These two triangles can be proved similar by the AA Similarity Theorem. This states that you need angles in a pair of triangles to be congruent to prove they are similar.

In line 2, the angles are proved congruent because they are alternate interior angles.

In line 3, the angles are proved congruent because they are vertical angles. 

In line 4, you state the reason they are similar. (AA)