3D Cuboid and the 3D Pythagorean Theorem

This GeoGebra example visualizes the 3D Pythagorean relationship in a cuboid: given its length, width (breadth), and height, it computes/illustrates how the space diagonal length is determined by the three perpendicular dimensions. It emphasizes the underlying structure from right triangles and extends the familiar 2D Pythagorean Theorem to three dimensions. The construction uses core geometry tools—Point, Segment, Polygon, Vector, and Midpoint—to place vertices, draw edges and key diagonals, form relevant faces, and represent diagonal directions whose magnitudes correspond to the needed distances. Dimension parameters such as length/height/breadth are adjustable, while Move and scale support dynamic exploration, helping learners verify the theorem visually and understand the metric dependency of the diagonal. Suitable for middle/high school solid geometry, vector/length intuition, and classroom demonstrations or self-study.