Question

in the given fig. QS bisector PR and PQ = QR . show that triangle PQS congruent triangle RQS

Answer 1

Answer:

Here is your answer In ∆PQS and ∆PRT, <P = <P (Common) PQ = PR (Given) <Q = <R (Given) Therefore, ∆PQS Congruent ∆PRT (A.S.A rule) Hence, => QS= RT (C.P.C.T)

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Answer 2

Both the Triangles are Congruent.

GIVEN: A triangle PQR such that PS = RS and PQ = QR

TO PROVE: Triangle PQS is congruent to Triangle  RQS

PROOF: According to the question,

We are given as,

In Triangle PQS and Triangle RQS, the following elements are equals,

PQ = QR                              ( Given in the question)

QS = QS                              ( Common line segment in both the Triangles)

PS = RS                               ( Given in the question.)

Therefore ,

Both the triangles are congruent by Side Side side rule.

Triangle PQS is congruent to Triangle  RQS.

As all three sides of both the Triangles are equal respectively.

Hence Proved.

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