Angles in a Semicircle: Visualizing the Thales' Theorem

①This GeoGebra example dynamically demonstrates the angle properties in a semicircle, particularly that the angle subtended by a diameter is always a right angle (Thales' theorem), and explores how other angles within the semicircle vary. ②Core mathematical concepts include the inscribed angle theorem, the right angle in a semicircle, triangle angle sum, and geometric transformations. ③Construction highlights: using GeoGebra commands such as Circle, Point, Segment, Angle, Vector, Mirror, CircumcircleArc, CircleSector, and Polygon to build the semicircle, auxiliary lines, and symmetric elements; a draggable point or slider allows real-time exploration of angle changes. ④Suitable for middle school (grades 8-9) or high school students, ideal for inquiry-based learning of circle geometry, teacher demonstrations, or student self-study.