Question

In the adjoining figure ABCD is a parallelogram and X Y are the points on he diagonals BD such that DX=BY . prove that CXAY is a parallelogram

Answer 1

Given : ABCD is a parallelogram X and Y are points on diagonal BD such that DX= BY.

To prove : AXCY is a parallelogram.

Construction : Join AC to meet BD at O.

Proof : We know that diagonals of a parallelogram bisect each other.

∴ OB = OD ...(1)

But BY = DX ...(2)

Subtracting (2) from (1) we get

OB – BY = OD – DX

⇒ OY = OX

Thus in quadrilateral AXCY diagonals AC and XY are such that OX = OY and OA = OC

i.e. the diagonals AC and XY bisect each other .

Hence CXAY is a parallelogram.