Question

In the given figure, if OA = BO and OC = OD, then, $\Delta AOD$ $\cong$ $\Delta BOC$ by which congruence rule ?

• A. AA
• B. SSS
• C. SAS
• D. SSA

Answer 1

The correct option is C SAS

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.