Question

In the given figure, PS 1) Prove that triangle PSQ is congruent to triangle PSR. 2) Is angleRPS is equal to angleQPS? Give Reasons

Answer 1

1.
PR=PS (given)
angle PSR=angle PSQ (each of 90°)
PS=PS(common)
Hance ∆PSR is Congurent to ∆PSQ

2.
angle RPS=angle QPS (c.p.c.t)


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Answer 2

IN ∆PRS and ∆PQS,

== angle PRS = angle PQS (angle opposite to equal sides are equal)

== angle PSR = angle PSQ (each 90 °)

== PR = PQ (given)

Therefore ∆PRS and ∆PQS are congruent (AAS)

angle RPS =angle QPS (by C.P.C.T.)

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