Constructing the Midpoint and Perpendicular Bisector of a Segment

This example demonstrates how to construct the midpoint of a given segment and then build its perpendicular bisector, illustrating the key fact that points on the perpendicular bisector are equidistant from the segment’s endpoints. The main math ideas include the definition of a midpoint, the properties of the perpendicular bisector (passes through the midpoint and forms a right angle with the segment), and using circle intersections to enforce equal distances. Construction workflow in GeoGebra: create points (Point / PointIn) for endpoints and intermediate points; represent the segment (Segment) and use Circle centered at each endpoint with the same radius; compute the intersections of the two circles (Intersect) to obtain two symmetric points; draw the perpendicular bisector as a line through those intersection points (Line); and use Distance (optionally Angle) to verify equal distances to both endpoints and the perpendicular relationship. The setup supports guided activities with and without GeoGebra and is suitable for middle/high school geometry and geometry-construction practice.