Sarthaks Test
+1 vote
561 views
in Mathematics by (29.7k points)

In the figure, the side QR of ∆PQR is produced to a point S. If the bisectors of ∠ PQR and ∠ PRS meet at point T, then prove that ∠QTR = 1/ 2 ∠QPR.

1 Answer

+1 vote
by (128k points)
selected by
 
Best answer

Exterior ∠PRS = ∠PQR + ∠QPR 

[Exterior angle property] 

Therefore, 1 2 ∠PRS = 1 2 ∠PQR + 1 2 ∠QPR 

⇒ ∠TRS = ∠TQR + 1 2 ∠QPR …(i) 

But in ∆QTR, 

Exterior ∠TRS = ∠TQR + ∠QTR …(ii) 

[Exterior angles property] Therefore, from (i) and (ii) 

∠TQR + ∠QTR = ∠TQR + 1 2 ∠QPR 

⇒ ∠QTR = 1 2 ∠QPR Proved.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...