Question

If the angle bisector of a triangle bisects the opposite side, then what type of triangle is this

Answer 1

if the angle bisector is from vertex A to side BC meeting it in, say P, then by the angle bisector theorem AB/AC=BP/PC. If P happens to be the mid-point of BC then BP=PC which makes AB =AC and the triangle is isosceles. Further, if BC =AB=AC then the triangle can be equilateral.