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Step 3: Pythagorean Triples

    A Pythagorean triple is any group of three integer values that satisfies the equation a2 + B2 = C2 is called a Pythagorean triple. therefore any triangle that has sides that form a Pythagorean triple must be a right triangle. When all three sides are whole numbers  you have a Pythagorean triple. For example A = 3 B = 4 C = 5 this can also be called a 3,4,5 triangle. Here is how you do the equation for example 3 squared plus 4 squared = 5 squared, in other words 9 + 16 = 25 therefor because these are all whole numbers the triangle must be a Pythagorean triple.

     There are four main Pythagorean triples families there is the 3,4,5, the 6,8,10, the 5,12,13, and the 8,15,17 triangles. If you multiply any of the three integers by the same amount you will still have a Pythagorean triple. For example 3,4,5, multiplied by two will give you 6,8,10, witch is a Pythagorean triple.

     Review- The integers represent the lengths of the sides of the triangles in a,b,c, order. If you do the equation and you don't come out with a whole number the integers are not a Pythagorean triple. Remember when multiplying Pythagorean triples families multiply all three numbers by the same amount.

Key words...

Pythagorean triple-A right triangle where the sides are in the ratio of integers. (Integers are whole numbers like 3, 12 etc)
integer-Includes the counting numbers {1, 2, 3, ...}, zero {0}, and the negative of the counting numbers {-1, -2, -3, ...}
Whole numbers-There is no fractional or decimal part. And no negatives.
Example: 5, 49 and 980 are all whole numbers.
Pythagorean triples families-every triple is a whole number multiple of the base triple.

<p>does the Pythagorean theorem have 3 whole numbers? or the Pythagorean triple have 3 whole numbers? Can Pythagorean theorem have a non perfect whole number? or can Pythagorean triple have a non perfect whole number?</p>
<p>does the Pythagorean theorem have 3 whole numbers? or the Pythagorean triple have 3 whole numbers? Can Pythagorean theorem have a non perfect whole number? or can Pythagorean triple have a non perfect whole number?</p>
You mistake in the Pythaborean triples : You say there are four basic sets; that is not true there are an infinite set.<br>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).<br>A set could be 7,24,25 (you could take it as the third set).<br>There is a wiki about &quot;formulas for generating pythgorean triples&quot;. (of which i derived the set here with the 7 ;)<br><br>One of the rules (from Euclides) : <br>-take an uneven number (a)<br>-square it. You get an uneven number.<br>-take the two concutive numbers that sum up to the square. These are b (the smallest, even) and c (de lagest, uneven).<br>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.<br>Overall a nice instructable<br><br>
<p>exactly dude (6,8,10) is not a primitive pythagorean triplet)</p>
<p>Here are some free printable worksheets that you can use for practice working with the Pythagorean theorem: <a href="http://stemsheets.com/math/pythagorean-theorem-worksheet" rel="nofollow">http://stemsheets.com/math/pythagorean-theorem-worksheet</a></p>
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
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.
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
In step 2 you subtracted 36 from 144 and gave 112 as the answer. That should be 108.
Thanks so much that was a typo i'll fix it right away.
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!!<br><br>Thanks, cobalt420
Ya I have a suggestion, you spell siggestions, suggestions....lol<br>~Mr. Mackenzie
Teachable moments. <br /><br />Dewey would be so jazzed by what just happened in this thread.
What do you mean?<br>
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.<br /><br />And you're teaching in the process. <br /><br />Pedagogical theory jokes. They are neither funny nor properly "jokes". I apologize for the confusion. Carry on being awesome.
Thanks so much that really means alot and i' m really trying hard to win this contest.
haha, i just learned this a couple weeks ago from my teacher! through he explained it a little differently...
&quot;We want teachers to show off the HANDS-ON projects they use with their students.&quot;<br><br>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. <br><br>Good Luck!<br><br>
Thank you so much I've made the change and even put in some practice questions.
Thank you I will do that!<br>

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