Inscribed Angles in a Semicircle: Dynamic Theorem Verification

This example demonstrates the inscribed-angle property for a semicircle: when a point moves on the semicircular arc determined by a diameter, the corresponding inscribed (circumference) angles remain constant. Key concepts include semicircles and diameters, inscribed angles/cyclic quadrilateral angle relationships, isosceles-triangle reasoning, and angle measurement for proof by dynamic geometry. Construction focuses on GeoGebra tools and objects: Circle to define the circle, Point to place diameter endpoints and the moving arc point, Line to draw the diameter and connecting lines, Intersect to find intersection points, CircleArc to create the semicircular arc, Dilate to generate transformed auxiliary elements, Segment to represent sides, and Angle to compute and display the target inscribed angle(s). The activity is suitable for middle-school geometry, classroom demonstrations, and student exploration of classic circle theorems.