Question

In the parallelogram ABCD, the angles A and C are obtuse. Points X and Y are taken on the diagonal BD such that the angles XAD and YCB are right angles.

Prove that: XA = YC.

State whether the above statement is true or false.

• A. True
• B. False

Answer 1

The correct option is A True

In $△XAD$ and $△YCB$
$\angle XAD=\angle YCB$ (Given each ${90}^{\circ }$)
$AD=BC$ (Opposite sids of parallelogram are equal)
$\angle XDA=\angle YBC$ (Alternate angles of parallel lines AD and BC)
$△XAD\cong △YCB$ (ASA rule)
Thus, $XA=YC$ (Corresponding sides)