Geometry Help

Pythagorean Theorem

Today we will be discussing the Pythagorean Theorem, named after a famous Greek mathematician called Pythagoras. Pythagorean theorem is very useful in Geometry. See video of Pythagorean Theory here.

Pythagorean theorem explained


Pythagorean theorem

Let's look at the triangle shown here. It is a right angled triangle with side a perpendicular to side b. Side c is called the hypotenuse or the side opposite the right angle.

The Pythagorean Theorem states that, in any right angled triangle, the area of the square whose sides are given by 'c' is the same as the sum of the areas of squares of sides a and b. This is illustrated in the diagram shown.

Pythagoras Theorem

Remember, the Pythagorean Theorem only works in right angled triangles. The Pythagorean Theorem is summarized by the equation:

Pythagorean Theorem formula

However, most of the time, when you are using the Pythagorean Theorem, you would want to find c not c2. Therefore, using the Pythagorean Theorem, we take the square root of c which gives us:

Pythagorean Theorem equation

That's it. In order to find the length of the longest side of the right angled triangle, just take the square root of the sum of the other two sides squared.