EMAT 6700

by Brad Simmons

Angle Bisector

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.  


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