Question

the side QR of triangle PQR is produced to a point S . if the bisector of PQR and PRS meet a point T, then prove that QTR=1/2QPR​

Answer 1

Step-by-step explanation:

Given :- Bisectors of angle PQR and angle PRS

meet at point T.

To Prove :- Angle QTR = 1/2 angle QPR

Proof :-

Angle TRS = angle TQR + angle QTR ( Exterior angle property of triangles)

Angle QTR = angle TRS - angle TQR --------(i)

Similarly,

Angle SRP = angle QPR + angle PQR

Angle QPR + 2 angle TQR = 2 angle TRS ( As QT and RT are the angle bisectors)

Angle QPR = 2 ( angle TRS - angle TQR)

Angle QPR = 2 angle QTR [ From equation (i)]

Angle QTR = 1/2 angle QPR.

Hence proved.

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