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CBSE Class 9 Answered

In fig 6.44 , the side QR of triangle PQR is produced to a point S. If the bisectors of angle PQR and angle PRS meet at point T, then prove that angle= 1/2 angle QPR
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Asked by Santosh.kumar0317 | 24 Jun, 2019, 01:43: PM
answered-by-expert Expert Answer

In ΔQTR,

∠ TRS = ∠ TQR + ∠ QTR             Exterior angle theorem in a triangle

∠ QTR = ∠ TRS - ∠ TQR ......(I)


Also in ΔQPR,

∠ SRP = ∠ QPR + ∠ PQR                        


2∠ TRS = ∠ QPR + 2∠ TQR       ∠TRS and ∠TQR are the bisectors of ∠SRP and ∠PQR respectively


∠ QPR = 2 ∠ TRS - 2 ∠ TQR

∠ TRS - 2 ∠ TQR = 1/2 ∠ QPR .....(II)

From (I) and (II), we get

∠ QTR = 1/2 ∠ QPR

Answered by Sneha shidid | 25 Jun, 2019, 09:49: AM

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