Angle bisector
= 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.