Pythagoras' theorem
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.
\(25~\text{cm}^\text{2} = 9~\text{cm}^\text{2} + 16~\text{cm}^\text{2}\)
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: \(c^2 = a^2 + b^2\)