Given below are some triangles and lengths of line segments. Identify ray PM is the bisector of ∠QPR.

Solution:-

Given:

• Two triangles QMP and MRP
• Lengths of line segments: QM = 3.6, QP = 9, MR = 4, RP = 10

To prove: Ray PM is the bisector of ∠QPR.

Proof:

• "QM"/"QP" = 3.6/9 = 2/5" (Given from triangle QMP)
• "MR"/"RP" = 4/10 = 2/5" (Given from triangle MRP)
• "QM"/"QP" = "MR"/"RP" (From the previous two steps)
• By converse of angle bisector theorem, ray PM is the bisector of ∠QPR.