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

Explanation

Given ABCD is a parallelogram and AE = CF
Construction Join BD, meet AC at point O.
Proof Since, diagonals of a parallelogram bisect each other.

`therefore" "OA=OC`
and `" "` OD = OB
Now, `" "` OA=OC
and `" "` AE = CF`" "`[given]
`rArr" "OA-AE=OC-CF`
`rArr" "OE=OF`
Thus, BFDE is a quadrilateral whose diagonals bisect each other.
Hence, BFDE is a parallelogram. `" "`Hence proved.