Perpendicular Bisector of a Line Segment: Construction and Properties

This GeoGebra example dynamically demonstrates how to construct the perpendicular bisector of a line segment and visually verifies its key property: every point on the bisector is equidistant from the segment's endpoints. The core mathematical concepts involved include the midpoint of a segment, perpendicularity, intersections of circles, and angle measurement. The construction steps are: create segment AB using the Segment command, mark endpoints with Point; draw two circles centered at A and B with equal radii using the Circle command; find their intersection points C and D via the Intersect command; connect C and D with a Segment to form the perpendicular bisector; finally, use the Angle command to measure angles α and β to confirm the right angles, and add text1 for labeling. This example is suitable for middle school geometry lessons to illustrate the definition and properties of perpendicular bisectors, and can also serve as an introductory exercise for geometric construction or as a foundation for deriving line equations in coordinate geometry.