Copying an Angle

An angle can be constructed as a copy of a given angle using a compass and a straightedge.

The given angle can be copied in four steps.

Draw a Ray with Endpoint

D

To begin, draw a ray using a straightedge.

Draw Arcs Across the Rays

Next, place the needle point of the compass at the vertex of the angle. Then, draw an arc across the rays at any distance from the vertex. With the same compass setting, position the needle point at

D,

and draw an arc across the ray.

Draw an Arc With Radius

B C

and Center

E

Bring the compass back to the original angle. Adjust the compass to measure the distance between the rays at their points of intersection. With that measurement, return to the what is becoming the copy. Align the needle point of the compass onto the ray and the arc's point of intersection. Mark this distance onto the arc.

Draw a Ray From

D

Through

F

On the copy, the second ray can be drawn from the endpoint on the first ray. Draw a segment from this point through the marked position on the arc.

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