Question

The sides AB and CD of a parallelogram ABCD are bisected at E and F. Prove that EBFD is a parallelogram.

Answer 1

Given: In ||gm ABCD, E and F are the midpoints of the side AB and CD respectively.

DE and BF are joined.

To prove : EBFD is a ||gm.

Construction: Join EF.

Proof : $\because$ ABCD is a ||gm

$\therefore$ AB = CD and AB || CD

(Opposite sides of a ||gm are equal and parallel)

$\therefore$ EB || DF

and EB = DF

($\because$ E and F are mid points of AB and CD)

$\therefore$ EBFD is a || gm.