Question

IN THE FIGURE, THE SIDE QR OF TRIANGLE PQR IS PRODUCED TO POINT S . if bisector of angle PQR and angle PRS meet at point T then prove that angle QTR = 1/2 angle QPR​

Answer 1

Answer:

Step-by-step explanation:

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]