Angle Bisector

Definition: A line which cuts an angle into two equal halves

Try this Drag one of the orange dots at L or M and note that the angle bisector divides the angle LJM into two equal parts.

In general 'to bisect' something means to cut it into two equal parts. The 'bisector' is the thing doing the cutting.

In an angle bisector, it is a line passing through the vertex of the angle that cuts it into two equal smaller angles. In the figure above, JK is the bisector. It divides the larger angle ∠LJM into two smaller equal angles ∠LJK and ∠KJM.

The two smaller angles are adjacent angles because they share the common leg JK.

Try this Adjust the angle below by dragging an orange dot and see how the bisector always divides it in half.

See also Constructions: bisecting an angle to see how to bisect an angle with compass and straightedge.

Angle Bisector

Other angle topics

General

Angle Types

Angle relationships