Question

Prove that if a point in the interior of an angle is equidistant from the sides of the angle then it belongs to the angle bisector of the angle (Point on angle bisector converse theorem).

Answer 1

Answer:

Step-by-step explanation:

Given: <AOB and an interior point D.

Prove: a point, D, in the interior of an angle is equidistant from the sides of the angle, then it belongs to the angle bisector of the angle.

Join D to A and B, then;

OA ⊥ AD (right angle property)

OB ⊥ BD (right angle property)

AD = BD (angle bisector theorem)

<AOD = <BOD (congruent angle property)

ΔAOD = ΔBOD (congruence property of triangles)

Therefore, point D lies on the bisector of <AOB.