Paper and pencil construction

1. Draw any angle. Label the vertex point C.

 

 



2. Place the compass at the vertex. Draw an arc that intersects both sides of the angle. Label the intersections A and B.

 



 

3. Place the compass point at A. Draw an arc. Then place the compass point at B. Using the same compass setting, draw another arc.

 



4. Label the intersection D. Use a straightedge to draw a ray through C and D. This is the angle bisector.

I can test the angle bisector by folding the paper on ray CD. If rays AC and CB are on top of each other our construction was successful.

This can also be done using Geometers Sketchpad.