Pythagoras' theorem

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

Right angle triangle with hypotenuse labelled

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

Pythagorus theorem proof

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

25~\text{cm}^\text{2} = 9~\text{cm}^\text{2} + 16~\text{cm}^\text{2}

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 a, b and c then Pythagoras' theorem states: a^2 + b^2 = c^2

Right angle triangle with sides a, b and c labelled