Question:
E and F are points on diagonal AC of a parallelogram ABCD such that AE = CF. Show that BFDE is a parallelogram.
Solution:
Given $A B C D$ is a parallelogram and $A E=C F$
To show $O E=O F$
Construction Join $B D$, meet $A C$ at point $O$.
Proof Since, diagonals of a parallelogram bisect each other.
Thus, BFDE is a quadrilateral whose diagonals bisect each other. Hence, $B F D E$ is a parallelogram.
Hence proved.