# 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.