The two triangles in the figure are congruent | vedclass

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(C) In $	riangle OPQ$ and $	riangle OSR$,we are given $OQ = OR$.Also,$\angle POQ = \angle SOR$ because they are vertically opposite angles.To prove

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$OP = OS$

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(C) In $	riangle OPQ$ and $	riangle OSR$,we are given $OQ = OR$.Also,$\angle POQ = \angle SOR$ because they are vertically opposite angles.To prove the triangles are congruent by the $SAS$ (Side-Angle-Side) congruence criterion,we need another side adjacent to the angle $\angle POQ$ and $\angle SOR$ to be equal.The sides adjacent to the angles are $OP$ and $OQ$ in $	riangle OPQ$,and $OS$ and $OR$ in $	riangle OSR$.Since we already have $OQ = OR$,we need $OP = OS$ to satisfy the $SAS$ condition.Therefore,the condition $OP = OS$ is sufficient.

The two triangles in the figure are congruent using a congruence theorem. It is given that $OQ = OR$. Which of these conditions,along with the given condition,is sufficient to prove that the two triangles are congruent to each other?

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