To construct the perpendicular bisector of
AB:
- Draw two circles with the same radius and with centers at the endpoints of segment AB. The radius must be long enough for the two circles to intersect.
- Mark the points of intersection P and Q of the two circles.
- Draw line PQ. This is the perpendicular bisector of segment AB.
- Mark the intersection M of line PQ with segment AB. This is the midpoint of segment AB.
Why does this construction work?
Click on the Show Segments button. This will create four line segments, AP, AQ, BP, and BQ.
- Why are segments AP, BP, AQ, and BQ congruent?
- What can you say about triangles APQ and BPQ? Why?
- Triangles PMA and PMB are congruent. Why?
- What does this imply about segments AM and MB?
- What is the angle between line PQ and segment AB? Why?
- What can you conclude?
See how to use perpendicular bisectors to construct the circumcircle of a triangle.