#### Answer

1. Opposite sides of rectangles are congruent, so AF is congruent to CD.
2. Angles of rectangles are all 90 degrees, so F is congruent to E, for ABEF and BCDE are both rectangles.
3. It is given that FE and ED are congruent.
4. Thus, by SAS, AFE and BED are congruent.
5. CPCTC, so AE and BD are congruent.
6. CPCTC, so AE and BD are at the same angle, meaning that they are also parallel.