Question

Q.No.9. The side QR of a triangle PQR is produced to a point S. If the bisector of
PQR and Z PRS meet at point T, QPR (See given Figure), then prove that;
< QTR = LQPR
р.
A
Q
R
S​

Answer 1

Step by Step Explanation:

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