Pythagorean Theorem

What is the Pythagorean Theorem?

The Pythagorean Theorem describes a very important relationship between the sides of a right triangle.

A right triangle (sometimes called a right-angle triangle) is simply a triangle that contains a right angle. A right angle is typically denoted by a little box. A right angle is 90°.

In the picture to the left, the purple triangles are right triangles and we can see the little box that tells us this.

This GIF does a really cool job of explaining the Pythagorean Theorem.

The Pythagorean Theorem tells us that the sum of the squares with side lengths of the two smaller sides of a triangle equals the square of the hypotenuse of the triangle.

In the GIF, the green squares depict the area of the square that has the side length of b (which appears to be four units). The red squares depict the area of the square with side length a (which appears to be 3 units). When you add those two areas, you get the square whose side length is equal to c, the length of the hypotenuse.

Working with the Pythagorean Theorem

In the video below, we'll go through a few examples of how to work with the Pythagorean Theorem.

Uses for the Pythagorean Theorem

We'll use the Pythagorean Theorem when we are working with perimeter, volume, and surface area.

Check Your Understanding

(1) Find the lengths of x, y, and z in the following triangles.

(2) Find the length of the diagonal in the following rectangle.

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