Perpendicular Bisector and Equidistance Theorem (GeoGebra)

This example demonstrates the equidistance phenomenon by constructing the perpendicular bisector of a line segment: every point on (or constrained by) the perpendicular bisector has equal distances to the segment’s two endpoints. It focuses on core geometry ideas such as the perpendicular bisector as the locus of points equidistant from two given points, and the relationship between right angles/constructed angle constraints and distance equality. In GeoGebra, the construction uses commands including Segment to build the base segment and connecting elements (e.g., links related to AD and BD), Point to define key geometric objects (A, B, C, E, D), and Angle to enforce the necessary geometric constraints via auxiliary objects (f, g, α) and labeling (text1). Suitable for middle-school geometry instruction, interactive construction practice, and classroom demonstrations of locus and equidistance reasoning.