An angle bisector of a triangle is a segment, ray or line which divides an angle of the triangle into two congruent (equal in measure) parts.

Since all triangles have three angles, all triangles have three angle bisectors.

The three angle bisectors of any triangle intersect at a common location called the incentre.

The incentre of any triangle, whether it is an acute triangle, a right triangle, or an obtuse triangle, occurs inside the triangle.

To visually verify this statement, please select "SHOW ALL ANGLE BISECTORS" in the demonstration applet above, then drag the vertices to create acute, right and obtuse triangles.