Pythagorean Theorem

Remember from a previous topic that a postulate is a statement assumed to be true. A **postulate** is a statement that is accepted as true without proof. A **theorem** is a statement that can be proven true. Euclidean Geometry has many postulates and theorems that are integral to understanding the course.

One of the most famous theorems in Geometry is the Pythagorean Theorem. It is named after a famous Greek mathematician named Pythagoras and works with right triangles. Remember the sides of a right triangle have special names. The side opposite the right angle is called the hypotenuse. The two sides that form the right angle are called legs.

The **Pythagorean Theorem** states that the sum of the squares of the lengths of the legs equals the length of the hypotenuse squared. In otherwords,

**leg ^{2 }+ leg^{2 }= hypotenuse^{2}**

Triangles are named with three points, labeled with capital letters. The side opposite the vertex is named with the corresponding lower case letter, as in the triangle below.

The Pythagorean Theorem for the triangle above is stated: **a ^{2 }+ b^{2 }= c^{2}.**

** *Note:** Remember that the hypotenuse is the longest segment of a right triangle. The longest side of a triangle is always opposite the largest angle.