Pythagorean Theorem: Dynamic Area Verification

① This GeoGebra example dynamically demonstrates the Pythagorean theorem by constructing squares on the three sides of a right triangle, showing that the sum of the areas of the two smaller squares equals the area of the largest square. ② Core mathematical concepts include right triangles, square areas, area conservation, geometric proof of the Pythagorean theorem, and verifying algebraic identities through area comparison. ③ Construction details: Using GeoGebra commands such as Point, Segment, Polygon, Angle, and PointIn, the example builds a right triangle and squares on each side, marks the right angle, places interior points, and computes polygon areas with the Area command. Text objects (ans, text1, text3) display numerical area values and the verification result. The construction involves multiple polygons (poly4, poly5, poly6) and auxiliary points (J, K, L, M, N, O, P, Q, R), and includes fractions to represent area ratios. ④ This is suitable for middle school geometry lessons on the Pythagorean theorem, high school discussions of area-based proofs and algebraic identities, and for teachers creating interactive instructional materials.