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» » Pythagorean Theorem

Pythagorean Theorem


This man, is Pythagoras. He was one of the first Greek Mathematicians. He discovered an amazing property of the right triangle that we all now know and love as the Pythagorean Theorem.

This theorem is well known in Algebra and we study it in our Quadratics unit because we are working with squared terms. Take a look.

The Pythagorean Theorem

In any right triangle, the sum of the squares of the legs (2 shorter sides) is equal to the square of the hypotenuse (the longest side).

pythagorean theorem

Please Note: This theorem ONLY works for Right Triangles.

Let's start by taking a look at an example where we need to find the hypotenuse.

Example 1

In a right triangle, the length of one leg is 6 cm and the length of the other leg is the square root of 13 cm. Find the length of the hypotenuse.

pythagorean theorem

Now let's look at an example of a problem where we are asked to find the length of a leg of a right triangle.

Example 2

A ladder that is 16.5 feet tall is placed against the side of a tree. The base of the tree to the top of the ladder is a distance of 14 feet. How far is the ladder placed away from the base of the tree?

If word problems confuse you, the best thing you can do is draw a picture!

Pythagorean theorem

Are you ready to try one?

Practice Problem

1. One leg of a right triangle is 18 inches long. The hypotenuse is 24 inches long. Find the length of the other leg.

Answer Key

pythagorean theorem

Great Job! Now you are ready to continue your exploration of quadratic equations.

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