Question

The side QR of triangle PQR is produced to a point S . If the bisector of ∠PQR and ∠PRS meet at point T , then prove that∠QTR = ½ ∠QPR.

Answer 1

Answer:

Given, Bisectors of ∠PQRand ∠PRS meet at point T.

To prove: ∠QTR=21∠QPR.

Proof,

∠TRS=∠TQR+∠QTR (Exterior angle of a triangle equals to the sum of the two interior angles.)

⇒∠QTR=∠TRS−∠TQR --- (i)

Also ∠SRP=∠QPR+∠PQR

2∠TRS=∠QPR+2∠TQR

∠QPR=2∠TRS−2∠TQR 

⇒21∠QPR=∠TRS−∠TQR --- (ii)

Equating (i) and (ii),

∴∠QTR=21∠QPR   [henceproved]

Answer 2

Answer:

Step-by-step explanation:

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