Angle bisector

An angle bisector is a ray dividing an angle into two equal angles. For nonopposite unit vectors $u,v$, its internal direction is $u+v$: the dot products with $u$ and $v$ are equal. The direction $u-v$ bisects the external angle. The three internal angle bisectors of a triangle meet at the incenter, equidistant from its side lines. The angle bisector theorem relates each bisector to side-length ratios.