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Question
Q is a point on the side SR of a ∆PSR such that PQ = PR. Prove that PS > PQ.
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Solution
In triangle PSR, Q is a point on the side SR such that PQ = PR.
To proof that PS > PQ
Proof: In triangle PRQ,
PQ = PR ...[Given]
∠R = ∠PQR ...(i) [Angle opposite to equal sides are equal]
∠PQR > ∠S ...(ii) [Exterior angle of a triangle is greater than each of the opposite interior angle]
Now, from equation (i) and (ii), we get
∠R > ∠S
PS > PR ...[Side opposite to greater angle is longer]
PS > PQ ...[PQ = PR]
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