 Proof that a triangle has 180 degrees!!!  

Author  Message 

Dojo Admin
Number of posts : 154 Location : Probably somewhere near a computer Registration date : 20080812
 Subject: 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. _________________ ~Dojo
Last edited by Dojo on Wed Aug 13, 2008 6:12 pm; edited 1 time in total 

 
skittles School Math Nerd
Number of posts : 40 Age : 24 Location : Lost Registration date : 20080813
 Subject: 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.. 

 
Dojo Admin
Number of posts : 154 Location : Probably somewhere near a computer Registration date : 20080812
 Subject: Re: Proof that a triangle has 180 degrees!!! Wed Aug 13, 2008 6:12 pm  
 W/e changing _________________ ~Dojo


 
Urc Starting Member
Number of posts : 13 Age : 23 Location : IN UR MOM Registration date : 20080813
 Subject: 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 180x+180y+180z or 540(x+y+z). Plug in x+y+z=180 for 360 

 
AIME15 Hardcore TMF user
Number of posts : 163 Age : 22 Location : Pleasanton, CA Registration date : 20080813
 Subject: 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 (ba)^2. So: 2ab+b^2+a^22ab=a^2+b^2.
Therefore, a^2+b^2=c^2. 

 
AIME15 Hardcore TMF user
Number of posts : 163 Age : 22 Location : Pleasanton, CA Registration date : 20080813
 Subject: 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? 

 
Dojo Admin
Number of posts : 154 Location : Probably somewhere near a computer Registration date : 20080812
 Subject: 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 _________________ ~Dojo


 
herefishyfishy1 Developer
Number of posts : 36 Age : 24 Location : An insignificant little bluegreen planet 93 million miles from the sun Sol. Registration date : 20080816
 Subject: 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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 Subject: Re: Proof that a triangle has 180 degrees!!!  
 

 
 Proof that a triangle has 180 degrees!!!  
