The Pythagorean Theorem says that for any right triangle with perpendicular sides \(a\) and \(b\), and long side (hypoteneuse) \(c\), the equation \(a^2 + b^2 = c^2\) holds. We can see that this is true by considering the following diagram. You can drag the diamond to change the shape of the right triangles shown in yellow.

The big squares have the same size and the 4 right triangles that each big square contains also have exactly the same size, so the remaining space in each big square must have the same area. That means the areas of the pink square (\(a^2\)) and the green square (\(b^2\)) must add up to the area of the blue square (\(c^2\)).

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