The Pythagorean theorem in three dimensions Quick check
1) In three dimensions, the Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
2) The Pythagorean theorem can be extended to three dimensions by considering right-angled triangles formed by any three sides of a rectangular cuboid.
3) Let's say we have a rectangular cuboid with sides a, b, and c. The diagonal of the cuboid can be represented by d. According to the Pythagorean theorem, d^2 = a^2 + b^2 + c^2.
4) This means that the square of the diagonal is equal to the sum of the squares of the lengths of the three sides of the cuboid.
5) The Pythagorean theorem in three dimensions is often used in geometry, physics, and engineering to calculate distances, lengths, and dimensions of three-dimensional objects.