Inscribed Angle Theorem (Proof without Words)

① This applet demonstrates the Inscribed Angle Theorem through a dynamic 'proof without words': for any arc of a circle, the measure of an inscribed angle (vertex on the circle, sides as chords) is exactly half the measure of the corresponding central angle, and remains constant as the vertex moves along the arc. ② Core mathematical concepts include inscribed angles, central angles, arc measures, triangle angle sums, and geometric invariance. ③ Construction highlights: using GeoGebra commands such as Circle, Point, Segment, Intersect, CircleSector, AngularBisector, Vector, Translate, Angle, Ray, and CircleArc, the applet builds circle O with points A, B, E, etc., employs angle bisectors, vector translations, and circular sectors to dynamically illustrate the angle relationships, with color-coded angles (α, β, γ, δ). ④ Suitable for middle or high school geometry classes, ideal for intuitive understanding of the theorem without formal proof, and useful for inquiry-based learning or teacher demonstrations.