Converse of Angles in the Same Segment - Dynamic Demonstration

This GeoGebra example dynamically demonstrates the converse of the theorem 'angles in the same segment are equal': if two angles subtending the same chord are equal, then their vertices must lie on the same arc of a circle. The core mathematical concepts include the inscribed angle theorem, its converse, concyclic points, and the idea of locus in dynamic geometry. The construction uses commands such as Circle to create the base circle, Intersect to find intersection points, DynamicCoordinates to allow moving points, Angle to measure angles α and β, Segment to draw connecting segments, and If with located to verify the condition of the converse theorem. This example is suitable for middle or high school geometry classes, helping students understand the converse of the inscribed angle theorem, observe how angle measures change as points are dragged, and develop geometric intuition and logical reasoning.