Visual Proof of the Pythagorean Theorem (Example 82, New Curriculum)

This applet demonstrates a visual proof of the Pythagorean Theorem, corresponding to Example 82 in the new national curriculum for compulsory mathematics education. Through dynamic geometric transformations including polygon rotations and translations, the applet vividly illustrates that the sum of the areas of the squares constructed on the two legs of a right triangle is exactly equal to the area of the square constructed on the hypotenuse. The construction employs fundamental geometric objects such as points, line segments, and polygons, and leverages rotational transformations to create an intuitive, step-by-step demonstration. Students can interact with the applet to observe how the two smaller squares reconfigure and rearrange to perfectly fill the larger square on the hypotenuse, providing a compelling visual verification of the theorem. This interactive approach supports middle school geometry instruction and student exploration, making an abstract algebraic relationship tangible and accessible. The applet is designed for classroom use in grades seven through nine, aligning with the curriculum standards for geometric proof and reasoning, and serves as an effective teaching aid for helping learners develop both intuitive understanding and rigorous proof skills in Euclidean geometry.