Pythagorean Theorem

Contributor: Jody Muth. Lesson ID: 13132

Can you use a math equation to find the quickest way home or to buy a new TV? Pythagoras says you can! Learn all about the Pythagorean theorem with this quick lesson.


Middle School

learning style
personality style
Grade Level
Middle School (6-8), High School (9-12)
Lesson Type
Quick Query

Lesson Plan - Get It!


What is the Pythagorean theorem? No, it's not a new dance craze or type of cellphone.

dancer and cell phone

Continue on to find out exactly what it is and how it can affect your daily life.

What is the Pythagorean theorem?

It is an equation discovered by Pythagoras that is used for right triangles. It states that when one angle in a triangle measures 90 degrees, the legs of the triangle (or short sides) when squared are equal to the hypotenuse (long side) squared. Here is an example of the formula:

right triangle

a2 + b2 = c2

Sound complicated? It's really not when you see it in action, so watch Math Antics - The Pythagorean Theorem:


Let's try an example ourselves.

If we look at the right triangle above again knowing that the short sides (legs) are 3 cm and 4 cm, how do we find out what the length is of the long side (hypotenuse)?

right triangle example

We know that the legs, a and b, are 3 cm and 4 cm. We DO NOT know what c is, so let's solve for it.

  a2 + b2 = c2
  32 + 42 = c2
  + 16 = c2
      25 = c2
      √25 = c
      5 = c



We can now say that the long side (hypotenuse) of the right triangle is 5 cm long!

Why do we need the Pythagorean theorem?

The Pythagorean theorem is used in geometry. As the video explained, it allows you to find the missing length of a right triangle. It also proves if a triangle is in fact a right triangle.

  • So why might that be important?

It is used by builders and architects every day to build homes and businesses. Although you may not be building or designing your first home yet, you need to be aware of how the theorem works for geometry class as well as how it may affect your life before you enter the real world (aka become an adult).

Check out Math Shorts Episode 15 - Applying the Pythagorean Theorem from PlanetNutshell to see an example of the Pythagorean theorem at work:


Ready to head over to the Got It! section to practice what you have learned?

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