Question

in figure 6.25 side QR of triangle pqr is produced to as if the bisector of angle pqr and angle PRS meet at point Tthen prove that angle qtr is equal to half angle QPR

Answer 1

To prove: Angle QTR = ½ angle QPR

Let angle TRS = a
Angle PRQ = 180 – 2a
Let angle TQR = b
Therefore, angle PQT = b
In triangle QPR
Angle QPR = 2a – 2b = 2 (a – b)
Similarly, in triangle QTR
Angle QTR = a – b

Therefore, angle QTR = ½ angle QPR
Hence prove.

Answer 2

Hello mate ☺

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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______❤

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