Chapter 13

The Pythagoras Theorem

Using a² + b² = c² to find the sides of a right-angled triangle — with an interactive exercise.

In a right-angled triangle, the Pythagoras Theorem connects the three sides.

Theorem

$a^2 + b^2 = c^2$ where $c$ is the hypotenuse (the longest side, opposite the right angle).

Example: legs of 3 and 4 give a hypotenuse of $\sqrt{3^2 + 4^2} = \sqrt{25} = 5$.

Remember

  • The hypotenuse is always the longest side.
  • Common triples: (3, 4, 5), (5, 12, 13), (6, 8, 10).

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