E and F are points on diagonal AC of a parallelogram ABCD such that AE = CF. Show that BFDE is a parallelogram.

Question

Philoid · Accepted Answer

Join BD, meeting AC at O.

Since diagonals of a parallelogram bisect each other,

OA = OC and OD = OB.

So,

OA = OC and AE = CF,

OE = OF

Now, BFDE is a quadrilateral whose diagonals bisect each other.

Hence, BFDE is a parallelogram.