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What is the Pythagorean theorem?

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Quick answer

The Pythagorean theorem states that in a right-angled triangle, the square of the longest side (the hypotenuse) equals the sum of the squares of the other two sides: a² + b² = c². It lets you find an unknown side when you know the other two.

Key things to understand

  1. It only applies to right triangles — triangles with one 90° angle.
  2. The hypotenuse (c) is always the side opposite the right angle and is the longest side.
  3. Example: if a = 3 and b = 4, then c = √(9 + 16) = √25 = 5.
  4. It's used everywhere from construction and navigation to computer graphics and measuring distances.

People also ask

Who was Pythagoras?
An ancient Greek mathematician credited with the theorem, though the relationship was known to earlier civilizations like the Babylonians.
What is a Pythagorean triple?
A set of three whole numbers that fit the theorem, like 3-4-5 or 5-12-13.
Can it be used on any triangle?
No — only right triangles. For other triangles you'd use the law of cosines, a more general version.