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Answer :

In \(\triangle{AOD}\) and \(\triangle{BOC}\), we have,

Now, \(\angle{AOD}\) = \(\angle{BOC}\) ...(vertically opposite angles)

Also, \(\angle{DAO}\) = \(\angle{CBO}\) = \(90^\circ\)

and BD = BC ...(shown in the figure)

Therefore, \(\triangle{AOD}\) \(\displaystyle \cong \) \(\triangle{BOC}\) ...(SAS congruency test)

Hence, OA = OB ...(By CPCT)

Thus, we can say that, O is the mid-point of AB.

So, CD bisects AB.

Hence, proved

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