The angle bisector theorem is commonly used when the angle bisectors and side lengths are known. It can be used in a calculation or in a proof. An immediate consequence of the theorem is that the angle bisector of the vertex angle of an isosceles triangle will also bisect the opposite side.

Does angle bisector divides the opposite side?

An angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.

Does angle bisector of equilateral triangle bisect opposite side?

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