Question

In the figure ,the side QR of ∆PQR is produced to a point S.If the bisectors of angle PQR and angle PRS meet at point T,then prove that angle QRT=angle QPR​

Answer 1

Answer:

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

To prove: ∠QTR=  

2

1

​  

∠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  

⇒  

2

1

​  

∠QPR=∠TRS−∠TQR --- (ii)

Equating (i) and (ii),

∴∠QTR=  

2

1

​  

∠QPR   [henceproved]