6. In Fig. 6.44, 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 = QPR.
We have,
PQR is produced to a point S and bisectors of PQR and PRS meet at point T,
By exterior angle sum property,
PRS = P + PQR
Now,
................(i)
Since QT and QR are the bisectors of PQR and PRS respectively.
Now, in QRT,
..............(ii)
From eq (i) and eq (ii), we get
Hence proved