Math, asked by Asthadubey123, 1 year ago

in figure,the side QR of ∆PQR produced to a point S if the bisector of angle PQR and angle PRS meet at a point T then prove that angle QTR =1÷2 angle QPR

Attachments:

Answers

Answered by plutonia
21
see the image for the answer
Attachments:
Answered by Anonymous
8

Hello mate ☺

____________________________

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______❤

_____________________________❤

Similar questions