Question

ABCD is a parallelogram . X is midpoint of AD and Y is the midpoint of BC. Prove that XY and BD bisect each other.

Answer 1

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Answer 2

Hence proved that XY and BD bisect each other.

Step-by-step explanation

In $\Delta XDO$ &  $\Delta BYO$,$</strong></p><p><strong>\textrm{XD = YB}$  ( As x & Y are the mid points)

$\angle DOX$ = $\angle BOY$ , ( Corresponding angle)

$\angle XDO =$$\angle YBO$, (Alternate Interior angle)

$\Delta XDO$$\equiv$$\Delta BYO$  (By AAS)

So OX = OY    (By C.P.C.T.)

 & OD = OB    By C.P.C.T.)

Hence Proved.