Question

In the above figure, it is given that $BDEF$ and $FDCE$ are parallelograms. Can you say that $BD=CD$? Why or why not?

• A. Yes
• B. No
• C. May be
• D. Cannot be determined

Answer 1

Answer: (A)

Given:-

$ABC$ is a triangle. $D,EF$ are points on $BC,CA.AB$ taken in order. $BDEF$ anf $FDCE$ are parallelograms.

To Prove:-

$BD=CD$

Proof:-

In parallelogram $BDEF$,

$BD=EF\dots \left(i\right)$[Opposite sides of a parallelogram are equal.]

In parallelogram $FDCE$,

$CD=EF\dots \left(ii\right)$[Opposite sides of a parallelogram are equal.]

From $\left(i\right)$ and $\left(ii\right)$,

$BD=CD$

Hence, proved.