Q11 of 33 Page 108

ACBD is a quadrilateral. The two parallelograms ABCE and BADF are drawn. Let us prove that, CD and EF bisect each other.

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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