# Pythagorean Theorem

The name Pythagorean theorem came from a Greek mathematician by the named Pythagoras. Pythagoras developed a formula to find the lengths of the sides of any 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.

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IN THE PYTHAGOREAN TRIPLET RULE, IF ONE THE NUMBERS IS TWICE SOME NUMBER,THEN THE OTHER TWO NUMBERS MUST ADD UP TO TWICE THE SQUARE OF THE ROOT NUMBER
IN THE PYTHAGOREAN TRIPLET RULE, IF ONE THE NUMBERS IS TWICE SOME NUMBER,THEN THE OTHER TWO NUMBERS MUST ADD UP TO TWICE THE SQUARE OF THE ROOT NUMBER
walterr2 years ago
You mistake in the Pythaborean triples : You say there are four basic sets; that is not true there are an infinite set.
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

iamamomof53 years ago
Sorry to point this out, but in the first picture you describe the first triangle as A=3 and B=4, but in the second picture you describe it as A^2=16 and B^2=9. So I'm unsure if the two photographs are two different triangles, or if you made a mistake, but I think it would be less confusing if the two picture matched.
cobalt420 (author)  iamamomof53 years ago
Its all good i just put the picture for an example. Thanks anyway for the advise and don't forget to go vote for the cookie contest and the teacher contest
Phil B3 years ago
In step 2 you subtracted 36 from 144 and gave 112 as the answer. That should be 108.
cobalt420 (author)  Phil B3 years ago
Thanks so much that was a typo i'll fix it right away.
cobalt420 (author)  cobalt4203 years ago
All fixed!! Do you have any siggestions to make this ible better im trying to make it the best that it can be for the teacher contest!!

Thanks, cobalt420
3 years ago
Ya I have a suggestion, you spell siggestions, suggestions....lol
~Mr. Mackenzie
3 years ago
Teachable moments.

Dewey would be so jazzed by what just happened in this thread.
cobalt420 (author)  wilgubeast3 years ago
What do you mean?
3 years ago
John Dewey (of library organization fame) would have lauded you as an active learner. You are obviously putting in some great effort to win this contest, to the point of getting some math help and some English help. You're engaging in meaningful learning, and that learning is being assisted by a couple of awesome teachers.

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.
cobalt420 (author)  wilgubeast3 years ago
Thanks so much that really means alot and i' m really trying hard to win this contest.
3 years ago
haha, i just learned this a couple weeks ago from my teacher! through he explained it a little differently...
Mr. Noack3 years ago
"We want teachers to show off the HANDS-ON projects they use with their students."

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!

cobalt420 (author)  Mr. Noack3 years ago
Thank you so much I've made the change and even put in some practice questions.
cobalt420 (author)  Mr. Noack3 years ago
Thank you I will do that!