Question

In the given figure, the side QR of ∆PQR is produced to

a point S. If the bisectors of <PQR and <PRS meet at

point T, then prove that

<QTR = ½<QPR​

Answer 1

Answer:

Embankment on a river that keeps it in its channel 13. Large body of sea water 14. Dry area where sand dunes are found 15. Small hill of sand caused by the action of the wind 16. Flat plain formed by river deposits during time of flood

Answer 2

$\mathfrak\red{ANSWER}$

Given, Bisectors of ∠PQR and ∠PRS meet

at point T.

To prove;

∠QTR= 1/2 ∠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

⇒ 1/2∠QPR=∠TRS−∠TQR ---(ii)

Equating (i) and (ii),

∴∠QTR= 1/2 ∠QPR

[hence proved]