The side QR of triangle PQR is produced
to a point S. The bisector of angle P meet QR at T .prove that angle PQR + angle PRS = 2 angle PTR
Answers
Answered by
17
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______❤
_____________________________❤
Attachments:
Similar questions