Question

The side QR of a triangle PQR is produced to a point S if the bisector of angle PQR and Angle PRS meet at point T prove that angle QTR is equal to 1 by half angle QPR

Answer 1

IN TRIANGLE PQR
/_PRS=/_PQR+/_QPR
divide both side 2,we get
1/2/_PRS=1/2/_PQR+1/2/_QPR
/_TRS=/_TQR+1/2/_QPR. (1)
NOW IN TRIANGLE TQR
/_TRS=/_TQR+/_QTR. (2)
BY COMPARING (1) and(2),we get
/_TQR+/_QTR=/_TQR+1/2/_QPR
/_QTR=1/2/_QPR
HENCE PROVED

Answer 2

Hello mate ☺

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Solution:

∠PQT=∠TQR               (Given)

∠PRT=∠TRS               (Given)

To Prove:  ∠QTR=1/2(∠QPR)

∠PRS=∠QPR+∠PQR

(If a side of a triangle is produced, then the exterior angle is equal to the sum of two interior opposite angles.)

⇒∠QPR=∠PRS−∠PQR

⇒∠QPR=2∠TRS−2∠TQR

⇒∠QPR=2(∠TRS−∠TQR)

=2(∠TQR+∠QTR−∠TQR)                          (∠TRS=∠TQR+∠QTR)

(If a side of a triangle is produced, then the exterior angle is equal to the sum of two interior opposite angles.)

⇒∠QPR=2(∠QTR)

⇒∠QTR=1/2(∠QPR)

Hence Proved

I hope, this will help you.☺

Thank you______❤

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