Question

the side QR of a triangle PQR is produced to a point S . if the bisector of triangle PQR and Triangle PRS meet at point T QPR ( see given figure) then prove that triangle QTR 1/2 triangle QPR​

Answer 1

Answer:

In ΔQTR, ∠TRS is an exterior angle. ∠QTR + ∠TQR = ∠TRS ∠QTR = ∠TRS − ∠TQR (1) For ΔPQR, ∠PRS is an external angle. ∠QPR + ∠PQR = ∠PRS ∠QPR + 2∠TQR = 2∠TRS (As QT and RT are angle bisectors) ∠QPR = 2(∠TRS − ∠TQR) ∠QPR = 2∠QTR [By using equation (1)] ∠QTR = 1/2 ∠QPR

Step-by-step explanation:

Answer 2

Step-by-step explanation:

In AQTR, LTRS is an exterior angle.

LQTR +2TQR = LTRS 2OTR = 4TRS

LTQR (1) For APQR, 2PRS is an external

angle. 2QPR + 4PQR = PRS OPR+

2TQR 2TRS (As QT and RT are angle

bisectors) LQPR = 2(LTRS - LTQR) LOPR

2OTR [By using equation ()] LOTR =

1/2 2PR