1. We are told that AF is congruent to CE. 2. AD and CB are congruent, for opposite sides of parallelograms are congruent. 3. Since opposite angles of parallelograms are congruent and given that AC bisects angle A and angle C, angles 1 and 2 are congruent. 4. By SAS, AFD is congruent to BEC. 5. CPCTC, so angle AFD and angle BEC are the same angle. 6. Since alternate exterior angles are only congruent when lines are parallel, DF and EB are parallel.