Take points (x,0,0), (0,y,0) and (0, 0, z), x,y,z all positive. Consider the areas of the three triangles defined by a pairsl of these points and the origin. Now consider the triangle B defined by (x,0,0), (0,y,0) and (0, 0, z). The sum of squared areas of the three sides equals the square of the area of B. Indeed the Pythagorean theorem works in any dimension!
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