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Question 5
If Q is a point on the side SR of a ΔPSR such that PQ = PR, then prove that PS > PQ.

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Solution

Given in ΔPSR,Q is a point on the side SR such that PQ = PR.
To prove PS > PQ

Proof in ΔPRQPQ=PR [given]
R=RQR...(i)
[angles opposite to equal sides are equal]
But PQR>S ....(ii)
[exterior angle of a triangle is greater than each of the opposite interior angle]
from Eqs. (i) and (ii) R>S
PS>PR [side opposite to greater angle is longer]
PS>PQ[PQ=PR]

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