Question

State and prove the converse of angle bisector theorem.

Answer 1

The angle bisector theorem converse states that if a point is in the interior of an angle and equidistant from the sides, then it lies on the bisector of that angle. The incenter is the point of intersection of the angle bisectors in a triangle.

Answer 2

Statement :

If a point is in the interior of an angle and equidistant from the sides, then it lies on the bisector of the angle. ... Like perpendicular bisectors, the point of concurrency for angle bisectors has interesting properties.

Proof is attached.

Hope you will now understand.