Construction:
Join BD, meeting AC at O.
According to the question,
Since diagonals of a parallelogram bisect each other,
We get,
OA = OC and OD = OB.
And,
OA = OC and AE = CF,
OA – AE = OC – CF
OE = OF
So, BFDE is a quadrilateral whose diagonals bisect each other.
Hence, BFDE is a parallelogram.