Welcome to this deck on Pythagoras' Theorem. This famous mathematical rule is incredibly useful for working with right-angled triangles. We'll cover what the theorem is, how to use it to find the length of a missing side, and even how to apply it to problems in three dimensions.

Before we get to the theorem itself, let's be clear about the parts of a right-angled triangle. A right-angled triangle has one angle that is exactly 90 degrees. The side opposite this right angle is always the longest side, and it has a special name: the hypotenuse.

Pythagoras' theorem describes the relationship between the three sides of any right-angled triangle. If we call the two shorter sides 'a' and 'b', and we call the hypotenuse 'c', then the theorem states that 'a' squared plus 'b' squared equals 'c' squared.

It is absolutely crucial to remember which side is which when using the formula. The sides 'a' and 'b' are the two shorter sides that meet at the right angle. It doesn't matter which one you call 'a' and which you call 'b'. But 'c' must always, always be the hypotenuse, the longest side.