# At a Glance - Pythagorean Theorem

A long time ago, in ancient Greece, a brilliant guy named Pythagoras discovered something pretty amazing and useful.

## Pythagorean Theorem: *a*^{2} + *b*^{2} = *c*^{2}

In a * right triangle *the

**sum of the squares of the two legs equals the square of the hypotenuse.**

**Legs**(a and b): the sides of the triangle adjacent to the right angle. They don't need to be the same length in order for this theorem to work**Hypotenuse**(c): the side of the triangle opposite the right angle

So, let's break this down. If you **square each side of the triangle**, the sum of the areas of the two legs squared is equal to the hypotenuse squared.

Here you can see it with numbers:

The area of the two smaller squares is (3 × 3 = 9 cm^{2}) and (4 × 4 = 16 cm^{2}).

The area of the larger square is equal to (5 × 5 = 25 cm^{2}).

If you add the two smaller areas together, you get the area of the square of the hypotenuse (9 + 16 = 25 cm^{2}).

*Look Out**: Do not attempt this with obtuse or acute triangles. This awesome theorem only works for right triangles.*

#### Example 1

Find the missing side of this triangle. | The length of the hypotenuse is missing, and we are given the lengths of the legs. |

#### Example 2

Find the length of the missing side of this right triangle. | The length of a leg is missing, and we are given the lengths of the other leg and the hypotenuse. |

#### Example 3

Is a triangle with sides lengths of 4 cm, 7 cm, and 8 cm a right triangle? | If it is a right triangle, then the sum of the squares of the two smaller sides will equal the square of the largest side. |