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: