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# Question and Answer

## QuestionMathsClass 7

In Figure, $$PS$$ is the bisector of $$\angle P$$ and $$PQ=PR$$ .Then $$\Delta PRS$$ and $$\Delta PQS$$ are congruent by the criterion

（ ）
A. $$AAA$$
B. $$SAS$$
C. $$ASA$$
D. Both (B) and (C)

D
4.6
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4.6
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## Solution

In $$\Delta PRS$$ and $$\Delta PQS$$
$$PQ=PR$$ [Given]
$$\angle QPS = \angle RPS$$ [Given]
$$PS =PS$$ [Common]
Hence  $$\Delta PRS \cong \Delta PQS$$ [SAS criteria]
Also, In $$\Delta PRS$$ and $$\Delta PQS$$
$$\angle PQS=\angle PRS$$ (Angles opposite to equal sides)
$$PQ=PR$$ (Given)
$$\angle QPS=\angle RPS$$ (Given)
Therefore, $$\Delta PRS \cong \Delta PQS$$ (By ASA congruency criterion)
Hence, option (D) is correct.