Does Pythagoras’ theorem work for any triangle, or only right triangles? My friend tried it on a different triangle and got a weird answer.
The theorem depends on the 90° angle: the two shorter sides are perpendicular, so the squares on them exactly fill the square on the hypotenuse. For any triangle the general rule is the cosine rule, c² = a² + b² − 2ab cos C. When C is 90°, cos C is 0 and it becomes a² + b² = c².
Accepted answer
Only right triangles. The proof relies on the 90° angle to build squares on each side and show their areas add up exactly. For other triangles, you’d need the law of cosines instead, which has an extra term that accounts for the angle not being 90°.