Question

Which of the following is the statement below describing? If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.

Answer 1

That's the angle bisector theorem. 

Answer 2

Yes , it is a true statement that if a If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.

Consider a line AB bisected at point M .

∠Q MB=∠A M Q=90°

Consider a point Q on the angle bisector of line

In ΔQMB and ΔAMQ

∠QMB = ∠AMQ=90°

MQ is common.

As QM is perpendicular Bisector, so AM=MB

ΔQMB ≅ ΔAMQ [SAS]

QA=QB [CPCT]