Question

in figure 6.44 the side QR of triangle pqr is produced to point as if the bisectors of angle pqr and angle PRS meet at point p then prove that angle qtr is equal to half of angle QPR​

Answer 1

Answer:

Given, Bisectors of ∠PQRand ∠PRS meet at point T.

To prove: ∠QTR=21∠QPR.

Proof,

∠TRS=∠TQR+∠QTR (Exterior angle of a triangle equals to the sum of the two interior angles.)

⇒∠QTR=∠TRS−∠TQR --- (i)

Also ∠SRP=∠QPR+∠PQR

2∠TRS=∠QPR+2∠TQR

∠QPR=2∠TRS−2∠TQR 

⇒21∠QPR=∠TRS−∠TQR --- (ii)

Equating (i) and (ii),

∴∠QTR=21∠QPR   [henceproved]