Dynamic Verification of the Pythagorean Theorem with Semicircles and Reflection

This GeoGebra example visually demonstrates the Pythagorean Theorem through a dynamic geometric construction involving semicircles and reflection symmetry. It illustrates the fundamental relationship among the sides of a right triangle using area equivalence and geometric transformations. Key mathematical concepts include the Pythagorean identity, properties of semicircles on triangle sides, axial symmetry (reflection), and intersection-based point construction. The model is built using commands such as Polygon (to form the right triangle), Midpoint, Semicircle, Mirror (for reflection), Segment, Intersect, and Point to generate critical elements like vertices (A, B, C), midpoints (M), centers (O), and auxiliary lines. The floorN command ensures numerical stability. Ideal for middle school mathematics education, this resource supports inquiry-based learning of the Pythagorean Theorem, geometric transformations, and introductory GeoGebra construction techniques.