Visual Proof of the Pythagorean Theorem (Manual Translation & Rotation)

This interactive GeoGebra example provides a visual, wordless proof of the Pythagorean theorem using dynamic geometry. It demonstrates how the sum of the areas of squares on the legs of a right triangle equals the area of the square on the hypotenuse. Key mathematical ideas include right triangles, area equivalence, and invariance under rigid transformations. The construction employs commands such as Point, Intersect, Circle, Polygon, Translate, Rotate, and Angle to create auxiliary points (e.g., D_5, G, H), polygons (poly1–poly3), and transformed objects (k7–k12), enabling users to manually translate and rotate components to verify the area relationship. Ideal for middle school mathematics instruction and inquiry-based learning.