Question

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


CXAY is a ___.

• A. Trapezium
• B. Square
• C. Parallelogram
• D. Rectangle

Answer 1

The correct option is C Parallelogram

Since the diagonals of a parallelogram bisect each other,
$\Rightarrow OA=OC$
and $OD=OB$ ........(1)
$DX=BY$ ........(2) [given]
On subtracting (2) from (1), we get
$OD-DX=OB-BY$
$\Rightarrow OX=OY$
Thus $OX=OY$ and $OA=OC$.
$\Rightarrow$ Diagonals of quadrilateral CXAY bisect each other.
Here, we cannot prove that the angles of CXAY are right angles.

$\Rightarrow$ CXAY is a parallelogram
So, the correct answer is option (c).