Question

In the given figure, $AB$ and $CD$ intersect at ${}^{\prime }{O}^{\prime },OA=OB$ and $OD=OC$. Show that $△AOD\cong △BOC$.

Answer 1

Given: AB and CD intersect at point O.

$OA=OB$ and $OD=OC$

In $\Delta AOD$ and $\Delta BOC$,

$OA=OB$ ....(Given )

$OD=OC$ ...(Given )

$\angle AOD=\angle BOC$ ...(Vertically opposite angles )

$\therefore \Delta AOD\cong \Delta BOC$ ....(SAS test) $\left[henceproved\right]$