Question

If AO = CO, OB = OD and BA = DC in the given figure
then, find the angle of $△AOB$ that will correspond to $\angle C$ of $△COD$ is :

• A. $\angle$B
• B. $\angle$D
• C. $\angle$DOC
• D. $\angle$A

Answer 1

The correct option is D $\angle$A

Consider $△$COD and $△$AOB
AO = CO (Given)
OB = OD ( Given )
BA = DC (Given)
Hence $△$COD $\cong$ $△$ AOB
by SSS criterion for congruency of triangles.
When the triangles are equal then their corresponding parts are equal.

The angle that corresponds to $\angle$A in $△$AOB is $\angle$C in $△$COD.