Question

2) In the given figure, PQ = PR and ∆Q=∆R
:Prove that: QS = RT
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Answer 1

Answer:

In △PQR,PQ+PR>QR ∵ sum of the two sides is greater than the third side.

∴PQ+PR>QT+TR ∵QR=QT+TR

⇒PQ+PR>QT+TS .....(1) ∵TR=TS

In △QST,QT+TS>QS .....(2)

∴ from (1) and (2) we have

PQ+PR>QS

Hence proved

Answer 2

Answer:

Is it GIVEN: QS = RT ? Then only we can prove that tri PQR is an isosceles triangle.

PROOF:

In triangle PQS & tri PRT

Since, QS = RT

< QSP = < RTP ( each being 90°)

& < P = < P ( common angles)

=> tri PQS congruent to tri PRT ( AAS similarity corollary)

=> PQ = PR ( cpct)

Hence, tri PQR is an isosceles triangle

[ Hence proved]

Explanation:

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