In parallelogram ABCD, E is the mid-point of AD and F is the mid-point of BC. Prove that BFDE is a parallelogram.

Given:

Parallelogram ABCD in which E and F are mid - points of AD and BC.

To prove:

BFDE is a parallelogram

Proof:

E is the mid-point of AD.

DE = $\dfrac{1}{2}$ AD

Also, F is the mid-point of BC.

BF = $\dfrac{1}{2}$ BC

But as we know opposite sides of parallelogram are equal.

So, AD = BC

Therefore, DE = BF

And, also AD is parallel to BC.

So, DE is parallel to BF.

When DE = BF and DE is parallel to BF. (opposite sides are equal and parallel to each other)

Hence, BFDE is a parallelogram.