Question

In fig, the side QR of A PQR is produced to
point s
s. If the biscators of Lear and LPRS
meet at point T then prove that LQTR = 1/2 LOPR.
P
Q
R
م)​

Answer 1

Answer:

Given: In a fig, the side QR of ΔPQR is produced to a point S.

The bisectors of ∠PQR and ∠PRS meet at point T.

To Prove: ∠QTR=21∠QPR.

Proof:

∠PRS=∠PQR+∠QPR ....(1)

(Sum of interior opposite angles is equal to the exterior angle).

∠TRS=∠TQR+∠QTR ....(2)

⇒2∠TRS=2∠TQR+2∠QTR

⇒∠PRS=∠PQR+2∠QTR

(OT bisects ∠PQR and RT bisects ∠PRS)

∠PQR+∠QPR=∠PQR+2∠QTR

(From 1 and 2)

⇒∠QPR=2∠QTR

or ∠QTR=21∠QPR [henceproved]