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.

Answer 1

Given : ABCD is a parallelogram and AX and CY are $\perp$ on diagonal BD

Now In $\Delta$ ABX and $\Delta$ CDY

$\to \angle AXB=\angle CDY={90}^0$ (Given)

and $\angle ABX=\angle CDY$ (Alternate opposite angles)

AB = CD (opposite sides of a ||gm)

$\Delta ABX\cong \Delta$ CDY (by AAS congruency criterion)

$\to AX=CY$

(C.P.C.T.)