Question

Side QR of Triangle PQR is produced to Point S. The bisector of P meets QR at T. Proof that Angle PQR+ Angle PRS= 2 Angle PTR

Answer 1

Answer:

Step-by-step explanation:

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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