**Introduction to the Pythagorean Theorem Notes**

The **Pythagorean Theorem** is a formula for right triangles. In the real world, it was used in the construction of the Parthenon. We’ll discover additional uses as we work through the chapter.

The Pythagorean Theorem deals __ONLY__ with __Right__ Triangles. You __cannot__ assume that a triangle is a right triangle by looking at it. Right triangles are indicated by a __box__ in one of the angles OR by a __90__° marking.

The side __across__ from the 90° angle is called the __hypotenuse__. It is always the __longest__ side. The other two sides are called __legs__.

Image used via creative commons license from: http://go.osu.edu/CzCn

In the Pythagorean Theorem the __legs__ are referred to as __A__ and __B__. The __hypotenuse__ is referred to as __C__.

The Pythagorean Theorem is used to find the __length__ of one of the legs or the hypotenuse. You may also determine if a triangle is a right triangle by plugging its __side__ lengths into the formula and __solving__. If it creates a __solution__, it is a __right__ triangle.

The formula is: a^{2} + b^{2} = c^{2 }

In the “real world” one application might be to find the height of a ladder leaned against a house. The house makes a right angle with the ground, where the ladder makes up the hypotenuse.

**For additional explanations, watch the following videos:**

The first video provided visual explanations of right triangles and their parts, as well as the Pythagorean Theorem. It also has example problems and extra practice. It is a good idea to watch through to the end if you’re wondering where this theorem came from!

The second video breaks down where the Pythagorean Theorem came from. It provides pictures showing why each side gets squared when using the formula. In addition, there are examples and worked problems throughout the video.

The third video is more of a fun application video. It gives you the basic definitions of right triangles and their parts. The main part of the video is using the Pythagorean Theorem to solve a “real life” (in the case of the main character) problem.