Question

State whether the statement is true/false:

If the bisector of an angle of a triangle also bisects the opposite side, the triangle is isosceles.

• A. True
• B. False

Answer 1

The correct option is A True

$In△ANB\&△ANC:$

$\angle BAN=\angle NAC$(NA bisects$\angle A$)

$BN=NC$ (NA bisects BC)

$AN=AN$(common)

$\therefore △ANB\cong △ANC$ by ASS congruency

$\therefore$ $AB=AC$,

Hence,$△ABC$ is isosceles.

$\therefore$ the given statement is True.