Question

$E$ and $F$ are points on diagonal $AC$ of parallelogram $ABCD$, such that, $AE$ = $CF$. We can conclude that, $BFDE$ is a ____.

• A. Trapezium
• B. Parallelogram
• C. Rectangle
• D. Kite

Answer 1

The correct option is B Parallelogram

Given, $ABCD$ is a parallelogram and $AE=CF$

Since, diagonals of a parallelogram bisect each other.
$\therefore OA=OC$
And, $OD=OB$ ...(1)

Now, $OA=OC$
$\therefore AE+EO=OF+FC$

And, $AE=CF$ ...(given)
$\therefore AE+EO=OF+AE$
$\Rightarrow EO=OF$ ...(2)

From equations (1) and (2),
We can say that the diagonals of quadrilateral $BFDE$, $EF$ and $DB$, bisect each other.

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

Hence, $BFDE$ is a parallelogram.