wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

In Fig, 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 = 12 QPR .
1188002_c2589c4b7b6b4b439689552e63d97ee2.PNG

Open in App
Solution



In PQR,

PQR+QPR=PRS [Exterior angle property]

2TQR+QPR=2TRS [As TQ and TR are bisectors of PQR and PRS respectively]

QPR=2(TRSTQR) ...(1)

Now, in TQR,

TQR+QTR=TRS [Exterior angle property]

QTR=TRSTQR...(2)

From (1) and (2)

QTR=QPR2

Hence, Proved


flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Basic Properties of a Triangle
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon