Construct the Midpoint of a Line Segment

① This example demonstrates the classic Euclidean construction of the midpoint of a given line segment using only compass and straightedge tools (circles and lines in GeoGebra). ② Core mathematical concepts include the perpendicular bisector of a segment, properties of isosceles triangles, circle intersections, and the definition of a midpoint; by drawing two equal-radius circles centered at the segment endpoints, the line through their intersection points cuts the segment at its midpoint. ③ Construction details: from the summary, the commands used are Segment (to create segment AB), Circle (centered at A and B with equal radii), Intersect (to obtain intersection points X and Y), AngularBisector (or connecting XY to form the perpendicular bisector), and the final intersection with AB gives midpoint M; objects include A, B, X, Y, f, d, c, C, g, M, h. ④ Suitable for middle school geometry lessons, introductory compass-and-straightedge constructions, or basic GeoGebra practice, helping students understand the rigor and geometric reasoning behind midpoint construction.