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som dutt
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Asked: 2023-03-28T10:23:51+00:00 In:

In Figure PR > PQ and PS bisects ∠ QPR. Prove that ∠ PSR > ∠ PSQ.

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In Figure PR > PQ and PS bisects ∠ QPR. Prove that ∠ PSR > ∠ PSQ.

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 Figure PR > PQ and PS bisects ∠ QPR. Prove that ∠ PSR > ∠ PSQ.

      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]

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