Constructing an Angle Bisector

Constructing an Angle Bisector

How to construct an angle bisetor of the given angle.

Goal

Constructing an Angle Bisector: Goal

Goal:
Constructing the red ray
that bisects the given angle

How to Construct

Constructing an Angle Bisector: Step 1

Place the point of the compass
at the vertex of the given angle.
(red point)

Draw an arc.
(red arc)

Constructing an Angle Bisector: Step 2

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

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

Constructing an Angle Bisector: Step 3

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

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

Constructing an Angle Bisector: Step 4

Draw a ray that passes through the blue arcs.
(red ray)

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