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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