Pythagorean Theorem as in Euclid's Elements

This interactive construction visually demonstrates Euclid's classical geometric proof of the Pythagorean theorem from *Elements*. It constructs three squares on the sides of a right triangle and illustrates the area relationship that underpins the theorem. Key mathematical concepts include the Pythagorean theorem, properties of right triangles, and polygonal areas. The model is built using GeoGebra commands such as Segment, Polygon, Intersect, If, and ClosestPoint to generate auxiliary points (e.g., D, E, F, G, H, I), line segments (sAB, sBC, sAC), and composite polygons (plBCDE, plACGF, plABHI). Ideal for middle school geometry instruction, this applet helps students grasp the geometric foundation of the theorem through dynamic visualization and rigorous construction.