# 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.

## CPB Investigation 1

## Sketch

- Construct . Be sure to show the labels for points
*A*and*B*. Right click on the point to find these properties. - 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. - Construct a circle from center point
*B*to point*A.* - Construct line
*CD*where*C*and*D*are the points of intersections on the circles. - Construct point
*E, the point*of intersection of line*CD*and . - Construct point
*F*anywhere on line*CD*. - Hide the circles. Use the right-click menu on the circles.
- 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.