1. It is given that BE and FD are congruent and that EF and FD are congruent. 2. Thus, BE and EF are congruent by the transitive property. 3. DE is the median of ADC, so E is the midpoint of AC. 4. Thus, AE and EC are congruent. 5. Since the diagonals are of a quadrilateral and bisect each other (in other words, split each other into two), it is a parallelogram.