Question

Prove that $△$AOD $\cong$ $△$BOC.

Answer 1

In $△$AOD and $△$BOC, we have,

OA = OB (given)

OD = OC (given)

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

Therefore, $△$AOD $\cong$ $△$BOC (by SAS 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 SAS congruence rule.