Question

$ABCD$ is a parallelogram and $X,Y$ are the points on diagonal $BD$ such that $DX=BY$. Prove that $CXAY$ is a parallelogram.

Answer 1

$ABCD$ is a parallelogram.

We know that the diagonals of a parallelogram bisect each other.

So, $OA=OC$ and $OD=OB$

$\Rightarrow$ $OD=OB$ ---- ( 1 )

$\Rightarrow$ $DX=BY$ ---- ( 2 ) [ Given ]

Subtracting ( 2 ) from ( 1 ), we get

$\Rightarrow$ $OD-DX=OB-BY$

$\Rightarrow$ $OX=OY$

$CXAY$ is a quadrilateral whose diagonals bisect each other.

$\therefore$ $CXAY$ is a parallelogram.