Constructing a Congruent Angle

Constructing a Congruent Angle

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

Goal

Constructing a Congruent Angle: Goal

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

How to Construct

Constructing a Congruent Angle: Step 1

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

Draw an arc.
(red arc)

Constructing a Congruent Angle: Step 2

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).

Constructing a Congruent Angle: Step 3

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)

Constructing a Congruent Angle: Step 4

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.

Constructing a Congruent Angle: Step 5

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

Constructing a Congruent Angle: Finish

Then the constructed angle is cougruent to the given angle.