by Brad Simmons
Use geometer's sketchpad to construct an angle bisector.
1. Start by constructing angle A on your sketch. Select point A. Construct a ray with point A as the endpoint. Select point A again. Construct another different ray with point A as the endpoint.
2. Select one of the rays (side of angle A). Construct a point on the ray and name it point B. Select point A and point B. Construct segment AB.
3. Select point A and segment AB. Construct circle by center and radius.
4. Select circle A and the other side of angle A (the ray not containing point B). Construct point of intersection. Name the point C.
5. Select point C and segment AB. Construct circle by center and radius. Select point B and segment AB. Construct circle by center and radius.
6. Select circle B (blue circle) and circle C (red circle). Construct a point of intersection and name it point D.
7. Select circle A, circle B, circle C, and segment AB. Hide the objects. Select point A and point D. Construct ray AD.
8. Ray AD is an angle bisector of angle CAB. Furthermore, angle CAD is congruent to angle BAD.