Question

in the given figure,the side qr of triangle pqr is produced to a point s. if the bisector of angle pqr and angle prs meet at a point t,tuen prove that angle qtr=1/2 angle qpr

Answer 1

Trs=tqr+qtr (by exterior angle theorem)
qtr=trs-tqr---let him equation l st
Prs=pqr+qpr
2trs=2tqr+qpr
qpr=2trs-2tqr
qpr=2(trs-tqr)
qpr=2qtr. From equation l st
Divide both side by 1/2
So 1/2qpr=qtr
qtr=1/2qpr

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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