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 Proof that a triangle has 180 degrees!!!

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Dojo
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PostSubject: Proof that a triangle has 180 degrees!!!   Wed Aug 13, 2008 5:29 pm

We take as a fact that a circle has 360 degrees, the definition of degree.

Let us take a arbitary triangle as above.
We draw the incircle and the incenter, conected to the vertices:

We now have three triangles:


The sum of three triangles, with each triangle as x is 3x.
Now notice the big triangle is the the three little triangles minus the inner circle, or 360.

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Last edited by Dojo on Wed Aug 13, 2008 6:12 pm; edited 1 time in total
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PostSubject: Re: Proof that a triangle has 180 degrees!!!   Wed Aug 13, 2008 6:11 pm

Hah... don't you mean "Proof that a triangle has 180 degrees"?
I have a different way but seeing as how I am retarded at latex/asymtote..
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PostSubject: Re: Proof that a triangle has 180 degrees!!!   Wed Aug 13, 2008 6:12 pm

W/e changing

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PostSubject: Re: Proof that a triangle has 180 degrees!!!   Wed Aug 13, 2008 7:25 pm

Proof that a triangle has exterior angles adding up to 360

let x y and z be the interior angles. By dojo, x+y+z=180

the sum of the exterior angles is 180-x+180-y+180-z or 540-(x+y+z). Plug in x+y+z=180 for 360
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PostSubject: Re: Proof that a triangle has 180 degrees!!!   Wed Aug 13, 2008 8:55 pm

Proof of the Pythagorean Theorem.

It's so much easier with a diagram, but here goes:

Draw 4 identical right triangles, each rotated 90 degrees more than the previous. Form a square with them, with a hole in the middle and the hypotenuse as the side. So the area is c^2, because that's the hypotenuse.

We can calculate this another way: the four triangles have area 1/2ab, and the hole in the middle has area (b-a)^2. So: 2ab+b^2+a^2-2ab=a^2+b^2.

Therefore, a^2+b^2=c^2.
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PostSubject: Re: Proof that a triangle has 180 degrees!!!   Thu Aug 14, 2008 4:48 pm

THere are hunderds more proofs of the pythagorean theorem! How many can you find?
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PostSubject: Re: Proof that a triangle has 180 degrees!!!   Sun Aug 17, 2008 3:38 pm

Hmmm....
Maybe there should be a new thread on pythagoreas

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PostSubject: Re: Proof that a triangle has 180 degrees!!!   Sun Aug 17, 2008 4:20 pm

Umm... You can use the alternate interior angles theorem and the corresponding angles theorem to prove that a triangle has 180 degrees.
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