Construction: Angle Bisector

How to construct an angle bisector of the given angle: by using a compass and a straightedge (ruler).

Example

Given

Let's see how to construct an angle bisector
that bisects the given angle.

Construction

Place the point of the compass
at the vertex of the given angle.

Draw an arc
that passes through
the rays of the given angle.

Place the point of the compass
at the intersection of the ray and the gray arc.
(blue point)

Draw an arc
that seems to pass the middle of the angle.
(blue arc)

Without changing the radius of the compass,
place the point of the compass
at the other intersecting point.
(blue point)

Draw an arc (blue arc)
that passes through the previous arc.

Draw a ray
that passes through
the intersection of the arcs.

Then this blue ray
is the angle bisector of the given angle.