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.

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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]