Question

In the given figure, if AO = BO and OC = OD, then, $\Delta AOD$ $\cong$ $\Delta BOC$ by __ congruence rule.

Answer 1

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

OA = OB (given)

OD = OC (given)

$\angle$AOD = $\angle$BOC (vertically opposite angles)

Therefore, $\Delta AOD$ $\cong$ $\Delta BOC$ (by S.A.S. congruence condition)

Since $\angle$AOD and $\angle$BOC are the included angles for sides OA & OD and OB & OC respectively, we have the triangles congruent by using S.A.S. congruence rule.