Geometric verification of the Pythagorean theorem with a right triangle

① This GeoGebra example (Open Middle) demonstrates how the Pythagorean Theorem emerges from an interactive geometric construction using a right triangle and its associated figures. ② Key concepts include right triangles, angle measurement/constraints (e.g., angles α, β, γ), circle-based constructions, and visually verifying the square-length relationship tied to the theorem. ③ Construction highlights: Textfield and multiple InputBox controls (InputBox1–InputBox6) to parameterize lengths/angles; Point, Circle, and Intersect to place circle(s) and compute their intersection points; Polygon and Segment to form the main triangle and auxiliary regions/edges; Angle and InteriorAngles to display and track interior angles; Max and If to evaluate quantities and apply conditional logic for which configuration is emphasized or how parameters are chosen. ④ Suitable for middle and high school students and for classroom exploration, inquiry-based learning, and demonstration of geometric reasoning.