Question

Q.No.9. The side QR of a triangle PQR is produced to a point S. If the bisector of
ZPQR and Z PRS meet at point T, QPR (See given Figure), then prove that
QTR = QPR
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Answer 1

In ΔQTR,  

∠ TRS = ∠ TQR + ∠ QTR             Exterior angle theorem in a triangle  

∠ QTR = ∠ TRS - ∠ TQR ......(I)  

 

Also in ΔQPR,  

∠ SRP = ∠ QPR + ∠ PQR

 

2∠ TRS = ∠ QPR + 2∠ TQR       ∠TRS and ∠TQR are the bisectors of ∠SRP and ∠PQR respectively  

 

∠ QPR = 2 ∠ TRS - 2 ∠ TQR  

∠ TRS - 2 ∠ TQR = 1/2 ∠ QPR .....(II)  

From (I) and (II), we get  

∠ QTR = 1/2 ∠ QPR

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