Question

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

Answer 1

Given ABCD is a parallelogram and AE = CF

To show OE = OF

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]

$\Rightarrow OA-AE=OC-CF$

$\Rightarrow OE=OF$

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

Hence, BFDE is a parallelogram. [Hence proved]