The Pythagorean Theorem Only Works for Right Triangles – Dynamic GeoGebra Demo

This GeoGebra example dynamically demonstrates that the Pythagorean theorem (a² + b² = c²) holds only for right triangles. By dragging the vertices of the triangle, users can observe how the sum of the squares of two sides compares to the square of the third side: the equality is satisfied exactly when the triangle is right-angled, and fails for acute or obtuse triangles. The core mathematical concepts include right triangles, the Pythagorean theorem, side-angle relationships, and triangle classification. The construction uses GeoGebra commands such as Rotate, Angle, Ray, Point, and Segment, with objects labeled α, β, A, B, C, D, a, b, c, and LaTeX-based text elements (text1, text2, text3) that dynamically display the squared side lengths and the relationship. This resource is suitable for middle school to high school students learning the Pythagorean theorem and its converse, and is also useful for teachers in classroom demonstrations or for student-led exploration to understand the theorem's applicability and geometric intuition.