1. Since AB is parallel to DC, it follows that any corresponding angles are congruent, for they are cut by the same transversal, BE. 2. Thus, by the corresponding angles theorem, angles ABC and DCE are congruent. 3. It is given that BC and EC are congruent. 4. It is given that C is the midpoint of BE. 5. By the definition of midpoint, BC is congruent to CE. 6. Thus, by SAS, triangle ABC is congruent to triangle CED. 7. Thus, corresponding angles ACB and DEC are congruent. 8. Thus, lines DE and AC are at the same slope. 9. Lines at the same slope are parallel, so AC and DE are parallel.