Algebra and Pre-Algebra Lessons

Algebra 1 | Pre-Algebra | Practice Tests | Algebra Readiness Test

Algebra E-Course and Homework Information

Algebra E-course Info | Log In to Algebra E-course | Homework Calculator

Formulas and Cheat Sheets

Formulas | Algebra Cheat Sheets
» » 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.

Other Quadratic Equations Lessons You Might Like

Like This Page?


We would love to hear what you have to say about this page!

Top of the Page

Follow Algebra-Class

Algebra Class E-course Members


Sign Up for Algebra Class E-courses

Click here to retrieve a lost password.

Search This Site

Custom Search

Algebra Class Courses

algebra ecourse

algebra 1 review course

pre algebra ecourse

Algebra Class
Most Popular Pages

algebra practice test

algebra cheat sheets

algebra formulas

What People Are Saying...

"I'd like to start off by relaying my sincerest gratitude for your dedication in teaching algebra. Your methodology is by far the simplest to follow, primarily because you take the time to include the small steps in between that most other teachers leave out.

It helps to know why you are doing something. I am 45 and heading to college to get my BS in Business. I need to brush up, hence the visit to your site. Great Job!"

Jimmy - United States

"I stumbled onto your site after I found out that I needed to use some fundamental algebra for an assignment. Turns out I had forgotten some things and your great site helped me remember them like "that" (snap of fingers). The organization of the site let me find exactly what I was looking for so easily. Kudos to you for maintaining such a great resource for students of all ages!"

Tom - United States

"I just wanted to write and basically thank you for making such a wonderful website! I'm 20 years old and about to take a basic placement test for college. I wanted to brush up on my Algebra skills and I stumbled upon your site. I'm amazed at how simple you make it and how fast I'm remembering Algebra! I don't remember getting most of the answers right when I had an actual teacher in front of me teaching this. Thanks a lot!"

Elizabeth - United States

"I am a pensioner living in South Africa. I stumbled on your website, the best thing that could ever happen to me! Your course in Algebra has helped me a lot to better understand the different concepts. Thank you very much for sharing your skills for teaching math to even people like me. Please do not stop, as I am sure that your teachings have helped thousands of people like me all over the world."

Noel - South Africa

This is an amazing program. In one weekend I used it to teach my Grade 9 daughter most of the introductory topics in Linear Relations. I took her up to Rate of Change and now she can do her homework by herself.

Reg - United States

Connect and Follow Algebra Class

Copyright © 2009-2015 Karin Hutchinson ALL RIGHTS RESERVED