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Question

In Figure, \(PS\) is the bisector of \(\angle P\) and \(PQ=PR\) .Then \(\Delta PRS\) and \(\Delta PQS\) are congruent by the criterion
Question: In Figure, PS is the bisector of angle P and PQ=PR .Then Delta PRS and Delta PQS are congruent by the criterion(   )A. AAAB. SASC. ASAD. Both (B) and (C)
( )
A. \(AAA\)
B. \(SAS\)
C. \(ASA\)
D. Both (B) and (C)

Answer

D
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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.
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