Given below are some triangles and lengths of line segments. Identify in which figures, ray PM is the bisector of QPR.

(i) In PQR
QM/RM = 35/15 = 7/3 …..(i)
PQ/PR = 7/3……………….(ii)
From (i) and (ii) QM/RM = PQ/PR
y Converse of angle bisector theorem , Ray PM is the bisector of QPR.
(ii) InPQR
PR/PQ = 7/10……..(i)
RM/QM = 6/8……..(ii)
From (i) and (ii) PR/PQ ≠ RM/QM
Ray PM is not the bisector of QPR
(iii) In PQR
PR/PQ = 10/9………(i)
RM/QM = 4/3.6 = 40/36 = 10/9 ……..(ii)
From (i) and (ii) PR/PQ = RM/QM
By Converse of angle bisector theorem , Ray PM is the bisector of QPR.