Answer :

ABCE and BADF are given parallelograms with one same side AB as shown with different colors

CD and EF are diagonals of quadrilateral CEFD

Diagonals of a parallelogram bisect each other hence if we proved that CEDF is a parallelogram then it would imply that EF and CD bisect each other

AB || EC and AB = EC … opposite sides of parallelogram ABCE … (i)

AB || DF and AB = DF … opposite sides of parallelogram ABDF … (ii)

Using (i) and (ii) we can conclude that

EC || DF and EC = DF

As two opposites side of quadrilateral CEDF are equal and parallel the quadrilateral is a parallelogram

And as CEDF is a parallelogram diagonals EF and CD bisects each other

Hence proved

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