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Question:

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

OP=OS

∠Q=∠R

∠P=∠S

PQ=SR

Solution:

Given OQ=OR and △POQ ≅ △ROS
We know that, congruent parts of congruent triangles are congruent
∠POQ ≅ ∠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.