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jai kohli
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Asked: 2023-02-15T05:52:12+00:00 In:

PS is the bisector of ∠ QPR of ∆ PQR. Prove that QS/SR = PQ/PR.

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How to use the angle bisector theorem. How bisector is equal to the ratio of the other two sides.
Class 10th Maths EXERCISE 6.6,Page No:152, Questions No:1
NCERT Books for Session 2022-2023 are based on CBSE Board.

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      PS is the bisector of ∠ QPR of ∆ PQR. Prove that QS/SR = PQ/PR.

      A line RT is drawn parallel to SP, which intersects QP produced at T.
      Given that, SP bisects angle QPR, therefore
      ∠QPS = ∠SPR …(1)
      By construction,
      ∠SPR = ∠PRT(As PS II TR) …(2)
      ∠QPS = ∠QTR(As PS II TR) …(3)
      From the above equations, we have
      ∠PRT = ∠QTR
      ∴ PT = PR
      By construction, PS II TR
      In ΔQTR, by Thales theorem
      QS/SR = QP/PT ⇒ QS/SR = PQ/PR [∵ PT = TR]

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