If the bisectors of ∠ PQR and ∠ PRS meet at point T, then prove that ∠ QTR = 1/2 ∠QPR.
NCERT CLASS 9 CHAPTER 6 Exercise 6.3 Lines and Angels Question No. 6
Page No. 6
In Fig. 6.44, the side QR of ∆ PQR is produced to a point S.
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∠PRS is the exterior angle of △PQR.
Therefore,
∠PRS = ∠QPR + ∠PQR
⇒ 1/2 ∠PRS = 1/2 ∠QPR + 1/2 ∠PQR
⇒ ∠TRS = 1/2 ∠QPR + ∠TQR …(1)[∵ ∠TRS = 1/2 ∠PRS and ∠TQR = 1/2 ∠PQR]
∠TRS is exterior angle of △TQR
Therefore,
∠TRS = ∠QTR + ∠TQR …(2)
From, the equations (1) and (2), we have
∠QTR + ∠TQR = 1/2 ∠QPR + ∠TQR
⇒ ∠QTR = 1/2 ∠QPR