Prove to using the triangle inequality.
Using the fact and define the sum of angles in a triangle.
9th Maths EXERCISE 7.4, Page No:132, Questions No:5.
NCERT Books for Session 2023-2024 are based on CBSE Board.
In Figure PR > PQ and PS bisects ∠ QPR. Prove that ∠ PSR > ∠ PSQ.
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In ΔPQR,
PR > PQ [∵ Given]
Hence, ∠Q > ∠R [∵ In a triangle, longer, side has greater angle opposite to it]
Adding ∠RPS both sides,
∠Q + ∠RPS > ∠R + ∠RPS
⇒ ∠Q + ∠RPS > ∠PSQ [∵ ∠PSQ is exterior angle of triangle PSR]
⇒∠Q + ∠QPS > ∠PSQ [∵∠RPS = ∠QPS]
⇒∠PSR > ∠PSQ [∵∠PSR is exterior angle of triangle PQS]