Question

Points E and F lie on diagonal AC of a parallelogram ABCD such that AE = CF. What type of quadrilateral is BFDE ?

Answer 1

In parallelogram ABCD,

AC is its diagonal. E and F are points on AC such that AE = CF
Join EB, BF, FD and DE
Join also diagonal BD which intersects AC at O
$\therefore$ O is the mid-point of AC and BD
$\therefore$ AO = OC
But AE = CF
$\therefore$ AO - AE = CO - CF
$\Rightarrow$ EO = OF
But BO = OD ($\because$ O is mid-point of BD)
$\therefore$ Diagonals EF and BD of quadrilateral bisect each other at O.
$\therefore$ BFDE is a parallelogram.