# Constructing Perpendicular Bisectors

Author:
Bob Allen
Using Geogebra's freehand tools (segment, line, point, and circle), you will construct a perpendicular bisector. Then you will explore those properties.

## Sketch

1. Construct . Be sure to show the labels for points A and B. Right click on the point to find these properties.
2. Construct a circle starting at center point A and releasing the mouse with the cursor at point B. Point B should control the circle's radius. Move B around and note that the circle changes as well.
3. Construct a circle from center point B to point A.
4. Construct line CD where C and D are the points of intersections on the circles.
5. Construct point E, the point of intersection of line CD and .
6. Construct point F anywhere on line CD.
7. Hide the circles. Use the right-click menu on the circles.
8. Measure AF and BF using the "Distance or Length" tool.

## Investigate

1. Line CD is the perpendicular bisector of . Move points A and B. What's special about point E?

2a. Move point F up and down the line. What can you say about the any point on a segment's perpendicular bisector? 2b. Write a conjecture about any point on a segment's perpendicular bisector.