Using Geogebra's freehand tools (segment, line, point, and circle), you will construct a perpendicular bisector. Then you will explore those properties.
[list=1][*]Construct [math]\overline{AB}[/math]. Be sure to show the labels for points [i]A[/i] and [i]B[/i]. Right click on the point to find these properties.[/*][*]Construct a circle starting at center point [i]A[/i] and releasing the mouse with the cursor at point [i]B. [/i]Point [i]B[/i] should control the circle's radius. Move [i]B[/i] around and note that the circle changes as well.[br][/*][*]Construct a circle from center point [i]B[/i] to point [i]A.[/i][/*][*]Construct line [i]CD [/i]where [i]C[/i] and[i] D [/i]are the points of intersections on the circles.[/*][*]Construct point [i]E, the point[/i] of intersection of line [i]CD[/i] and [math]\overline{AB}[/math].[/*][*]Construct point [i]F[/i] anywhere on line [i]CD[/i].[/*][*]Hide the circles. Use the right-click menu on the circles.[/*][*]Measure [i]AF [/i]and [i]BF[/i] using the "Distance or Length" tool.[/*][/list]
1. Line [i]CD[/i] is the perpendicular bisector of [math]\overline{AB}[/math]. Move points [i]A [/i]and [i]B[/i]. What's special about point [i]E[/i]?
2a. Move point [i]F[/i] up and down the line. What can you say about the any point on a segment's perpendicular bisector?[br][br]2b. Write a conjecture about any point on a segment's perpendicular bisector.