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The Pythagorean Theorem

This is one of the most-used theorems in all of math, and it will take you from Geometry, Algebra and into even more advanced topics such as calculus. Luckily, it is also one of the simplest formulas and is very easy to remember.

The Pythagorean Theorem: a² + b² = c²

That's all there is to it!

But what does it mean? It has to do with triangles. Right triangles, to be exact. The diagonal line is always the "c" line, whereas either of the other two values can be assigned "a" or "b." (See graphic below.)

The theorem provides a very easy way to determine any side of the right triangle, as long as two sides are known.

This can also be used in real life situations - let's say that you can decide which route to take to get to your destination. You can get on road A, then turn onto road B, or you can just take road C all the way there. On road C you can travel 30 miles per hour, on roads A and B, you can only travel 20.

Using the Pythagorean Theorem, you can determine the lengths of each of the roads (assuming they form a right triangle), and decide which route will get you to your destination fastest!

Using the above triangle, if A was 5 and B was 6, then C² = 5² + 6². Thus, C = the square root of 61; roughly 7.81. Since you know each distance, the rest of the example uses other lessons such as the Distance Equations.

That does it for the Pythagorean Theorem. As you can see, it's very basic and very easy to remember - and it is widely used, so be sure to remember it! Choose another Math Topic or select a different subject in the Lesson Center!


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