# Constructing a Congruent Angle

How to construct an angle that is congruent to the given angle.

## Goal

Goal:
Constructing the red angle
that is congruent to the given angle

## How to Construct

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

Draw an arc.
(red arc)

Without changing the radius of the compass,
place the point of the compass
at the endpoint of the ray.
(red point)

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

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

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

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

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

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

Then the constructed angle is cougruent to the given angle.