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

Question

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

Philoid · Accepted Answer

Theorem: The bisector of an angle of a triangle divides the side opposite to the angle in the ratio of the remaining sides.

Therefore, we’ll find the ratio for all the triangle.Hence, for

(1)

= 2.33

And

= 2.33

⇒

⇒ In (1), ray PM is a bisector.

(2)

= 0.75

And

= 0.7

⇒

⇒ In (2), ray PM is not a bisector.

(3)

= 1.1

And

= 1.11

⇒

⇒ In (3), ray PM is a bisector.