Pythagorean Theorem Inequalities: Acute, Right, and Obtuse Triangles

This GeoGebra example demonstrates the Pythagorean theorem inequalities by showing how the relationship between the squares of the two shorter sides and the square of the longest side changes for acute, right, and obtuse triangles. The core mathematical concepts include the Pythagorean theorem, squared side lengths, triangle classification, angle comparison, and inequality reasoning. The construction uses Point, Segment, and Polygon to create triangles and side objects, Angle to mark the relevant angles, and Circle, Intersect, Rotate, and Ray to generate auxiliary circles, intersection points, and rotated figures. An If command dynamically displays the corresponding inequality result for each triangle type. It is suitable for middle-school or high-school geometry and algebra lessons, classroom exploration, student experiments, and visual demonstrations of Pythagorean inequalities.