The Pythagorean Theorem states that in a right triangle, the total of the squares of each of the triangle legs lengths is identical to the square of the triangle’s hypotenuse length.

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**This transcript is provided for your convenience**

A long long time ago, Pythagoras, a Greek mathematician, discovered a very interesting property of right triangles. If you add the squares of the triangle’s legs lengths, the outcome is equal to the square of the triangle’s hypotenuse length.

This property, that has so many applications in architecture, engineering, art, and science, is what we call the “Pythagorean Theorem”.

Let’s see how this theorem is helping you to learn more about how triangles are constructed. And the good thing is that you even don’t need to speak the Greek language to apply or understand the discovery of Pythagoras.

**The Pythagorean Theorem**

The Greek mathematician Pythagoras was studying right triangles and in what way the hypotenuse and the legs of right triangles were related before he derived his theory.

**The Pythagorean Theorem**

In case *a* and *b* symbolize the lengths of a right triangle’s legs and c symbolizes the hypotenuse’s length, then the sum of the squares of the leg’s lengths is the same as the square of the hypotenuse’s length.

This interesting relationship is represented in this formula: a² + b² = c²

In this box above, you could have noticed the expression “square,” but also the small “2”s to the top of the letters like in a² + b² = c². To square a number, we multiply that number it by itself. If we square, for example, the number “5”, we multiply 5 times 5; If we square “12”, we multiply 12 times 12. A few common squared numbers are shown in the following table.

When we see the following equation: a² + b² = c², we can see this as follows: “the length of the side with “*a”* times itself (so a²), plus the length of the side with “*b”* times itself (so b²) equals the length of the side with “*c”* times itself so c²).”

Let’s take a look at the Pythagorean Theorem using an example of a right triangle.

The Pythagorean theorem holds true for the right triangle above. The sum of both legs’ length squares (a² plus b²) equals the square of the hypotenuse’s length (c²). This actually is holding true for every right triangle!

This Pythagorean Theorem may be represented in terms of “area” as well. In all right triangles, areas of squares drawn from any hypotenuse equals the sum of areas of squares drawn from the triangles’ two legs. Just take a look at the following illustration in that same 3-4-5 right triangle.

Please note that this Pythagorean Theorem is ONLY working if we have *right* triangles.

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