Pythagoras’ theorem can be used to calculate the length of any side in a right-angled triangle. Pythagoras’ theorem can be applied to solve 3-dimensional problems.

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The longest side of a right-angled triangle is the **hypotenuse**. The hypotenuse is always opposite the right angle.

Draw a square on each side of a right-angled triangle. Calculate the area of each square.

The area of the largest square is the sum of the area of the other two squares.

This is **Pythagoras' theorem**.

Pythagoras' theorem states that, in any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares on the other two sides.

If the sides of the right-angled triangle are labelled , and then Pythagoras' theorem states: