Question

The two triangles in the figure are congruent by the congruence theorem. Here, it is given $OQ=OR$. Which of the following condition, along with the given condition, is sufficient to prove that the two triangles are congruent to each other?

• A. $\angle P=\angle S$
• B. $\angle Q=\angle R$
• C. $OP=OS$
• D. $PQ=SR$

Answer 1

Answer: (C)

$OP=OS$

Given $OQ=OR$ and $△POQ\cong △ROS$
We know that, congruent parts of congruent triangles are congruent
$\angle POQ\cong \angle ROS$ (vertically opposite angles)
If $OP=OS$ then by using the (SAS) congruent, we can conclude the congruency of two triangles.

Hence, option C is sufficient to prove the congruency.