In Fig. 6.44, the side QR of `triangle PQR` is produced to a point S. If the bisectors of `angle PQR` and `angle PRS` meet at point T, then prove that `angle QTR =1/2 angle QPR`.

In figure, the side QR of Delta PQR is produced to a point S. If the bisectors. of /_PQR and /_PRS meet at point T, then prove that /_QTR = 1/2 /_QPR .

In Fig. 6.15, angle PQR = angle PRQ , then prove that angle PQS = angle PRT .

If the bisector of an angle of a triangle also bisects the opposite side, prove that triangle is isosceles.

In Fig. 6.38, the sides AB and AC of Delta ABC are produced to points E and D respectively. If bisectors BO and CO of angle CBE and angle BCD respectively meet at point O, then prove that angle BOC = 90^@ -1/2 angle BAC .

In the fig. triangle AB=AC and bisectors of angleB and angleC meet at a point O. prove that BO=CO and the ray AO is bisector of angleA

In Fig 7.51, PR > PQ and PS bisects angle QPR . Prove that angle PSR > angle PSQ .

In a quadrilateral ABCD, AO and BO are bisectors of angleA and angle B respectively. Prove that angleAOB=1/2(angleC+angleD)

If the sides of a triangle are produced in order, then the sum of the three exterior angles so formed is

P is a point on the bisector of an angle angleABC . If the line through P parallel to AB meets BC at Q. prove that triangle BPQ is isosceles.