# What is a Theorem? - Definition & Examples

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• 0:00 Theorem Defined
• 0:38 The Pythagorean Theorem
• 1:24 Pythagorean Theorem Example
• 2:06 Triangle Sum Theorem
• 2:31 Triangle Sum Theorem Example
• 2:56 Lesson Summary
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Lesson Transcript
Instructor: Allison Petrovic

Allison has experience teaching high school and college mathematics and has a master's degree in mathematics education.

In this lesson, will learn the definition of a theorem. We will also go over the Pythagorean theorem and the triangle sum theorem. An example of each theorem in action will also be provided.

## Theorem Defined

Have you ever heard of the word 'theorem'? Maybe you've heard of the Pythagorean theorem or the Triangle Sum theorem. The word 'theorem' is quite common in mathematics. As you continue to middle school, and even into high school, you'll learn many new theorems in your math classes.

So what is a theorem? Put simply, a theorem is a math rule that has a proof that goes along with it. In other words, it's a statement that has become a rule because it's been proven to be true. This definition will make more sense as we look over two popular theorems in mathematics. Let's get started!

## The Pythagorean Theorem

The Pythagorean theorem might be one of the most well known theorems in mathematics. This theorem explains that if you add together the squares of the two legs of a right triangle, you'll get the square of the hypotenuse. The hypotenuse is the side of a right triangle that is opposite from the right angle. So if we have a right triangle, we can label one of the shorter sides as a, and the other shorter side as b. We also can label the hypotenuse or the longest side as c. The formula for the Pythagorean theorem is then: The Pythagorean theorem will only work for triangles with a right angle. Let's not forget that every theorem has a proof. While there are many interesting proofs for this theorem, in this lesson we're just looking at the main idea.

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