Circle Theorem 3 – Angles in the Same Segment

① This dynamic worksheet illustrates the 'angles in the same segment' circle theorem, showing that angles subtended by the same arc are equal. ② The core mathematical concepts involve central angles, chords, arcs, and inscribed angles, highlighting fundamental properties of circles. ③ The construction uses GeoGebra commands Circle, Point, Segment, and Angle to define a circle c and points A, B, C, D, and employs sliders to dynamically adjust point positions, generating angles α and β to verify the theorem. ④ It is suitable for high‑school geometry classes or early olympiad training, providing an intuitive visual aid for geometric proofs.