**right triangle**. Pythagoras Discovered that if he treated each side of a right triangle as a square (see figure 1) the two smallest squares areas when added together equal the area of the larger square. The formula is A2 + B2 = C2, this is as simple as one

**leg**of a triangle squared plus another leg of a triangle squared equals the

**hypotenuse**squared.

In this lesson I will teach you how to use the Pythagorean theorem, I will show where you put it to use and some different ways to use the theorem to find the lengths of legs when given the leg length and the hypotenuse length. I will try my best to explain every step of the way to my fullest and complete answer.

My inspiration for this instructable came from having the interest of finding how formulas work. I take interest especially in the Pythagoras theorem because we use it in lots of every day jobs such as engineering, woodworking and metalworking. I hope I can pass my interests on to you in this lesson.

Prescribed learning outcomes, by learning how the Pythagorean theorem works students will learn how to square, square root, add and subtract, and learn the Pythagoras formula.

Key words...

**Hypotenuse-**In geometry, a hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle.

**Leg**- Either sides of a right triangle that are opposite to the hypotenuse.

**Right triangle**- A triangle that has one corner of a ninety degree angle.

**Signing Up**

Secondly, you mention 3,4,5 (which is correct) followed by 6,8,10 which is no basic set (because all numbers are just the same multiple of 3,4,5).

A set could be 7,24,25 (you could take it as the third set).

There is a wiki about "formulas for generating pythgorean triples". (of which i derived the set here with the 7 ;)

One of the rules (from Euclides) :

-take an uneven number (a)

-square it. You get an uneven number.

-take the two concutive numbers that sum up to the square. These are b (the smallest, even) and c (de lagest, uneven).

Since there is an infinite set of prime numbers (who are no multiple of anything) to start with as a, this proves you have an infinite set of basic pythagorean triples.

Overall a nice instructable

Thanks, cobalt420

~Mr. Mackenzie

Dewey would be so jazzed by what just happened in this thread.

And you're teaching in the process.

Pedagogical theory jokes. They are neither funny nor properly "jokes". I apologize for the confusion. Carry on being awesome.

The above statement comes right from the contest description on the site. I recommend that you add a hands-on element to your lesson. Your steps are very thorough, but keep in mind that many students are kinesthetic learners, meaning they actually learn better by be being involved in a physical activity. Perhaps you could have students cut out or fold triangles as part of the lesson. Your lesson will be so much more effective if you come up with a creative gimmick.

Good Luck!