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

Solution:-

Given:

• Triangle PQR
• PR/PQ = 7/10 ……(i)
• RM/QM = 6/8 ……(ii)

To prove: Ray PM is not the bisector of angle QPR.

Proof:

• From (i) and (ii), we have PR/PQ ≠ RM/QM.
• Therefore, by the converse of the angle bisector theorem, Ray PM is not the bisector of angle QPR.
• Hence, the statement is proven.

Therefore, in triangle PQR with PR/PQ = 7/10 and RM/QM = 6/8, Ray PM is not the bisector of angle QPR.