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