Construction: Congruent Angle

How to construct an angle that is congruent to the given angle: by using a compass and a straightedge (ruler).

Example

Given

Let's see how to construct an angle
that is congruent to the given angle.

Let's use the bottom ray
to construct the congruent angle.

Construction

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

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

Without changing the radius of the compass,
place the point of the compass
at the endpoint of the bottom ray.

Draw an arc (blue arc)
just like the previous arc.

Place the point of the compass
at the intersection
of the given angle's ray and the gray arc.
(blue point)

The radius of the compass
is the distance
from the blue point to the other intersecting point.
(blue dashed arc)

Without changing the radius of the compass,
place the point of the compass
at the intersection
of the bottom ray and the gray arc.
(blue point)

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

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

Then the constructed bottom angle
is cougruent to the given angle.