Question

In the given figure, ABCD is a parallelogram, and X and Y are points such that DX=BY.Prove that:

• A. AXCY is a parallelogram
• B. AX=XY,AY=CX
• C. $\Delta AYB\cong \Delta CXD$
• D. $\Delta AXD\cong \Delta CYB$

Answer 1

The correct option is A AXCY is a parallelogram

Given ABCD is a parallelogram

and X and Y are points on diagonal BO such that DX$=$BY

$DB=OD$ ………..$\left(1\right)$

$BY=DX$ ………..$\left(2\right)$

substracting $\left(2\right)$ from $\left(1\right)$ 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., thus diagonals AC and XY bisect each other.

Hence CXAY is a parallelogram.