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Tuesday, November 22, 2005

Proof By Disproving all other Angles

Proof that the total of the degrees cannot exceed 180 or go below 180

Here is a right triangle with the two adjacent sides both being three units long

(A and C). In this triangle C + B + A = 180 degrees. Now if the triangle had 185 degrees…

As you can see the line off the 50 degree angle at c does not meet up with the endpoint of line C (And if you extended line C then the angle at the top would no longer be 45 degrees but 40 degrees. So it would still be a 180 degree figure). This would be true for any angle above 180 degrees. Then when it is below 180 degrees line B cuts through line C instead of meeting it at the endpoint. The angle where that meets it ends up being b – c = a (Assuming that you had b as the largest angle). Then if you input any of those into the formula a + b + c = 180 it works. (b – c) + b + c = 180 then you input the largest angle for b any angle for c that doesn't bring the total to 180 into that formula and you will get 180 unless your angle b is 180 or greater or sixty or less (sixty or less and b is not the greatest angle). Then you get a closed figure with three angles, a triangle. If you put anything greater than 180 for the total you get something like 180 = 181. You put something less than 180 than you get something like 180 = 179 which is completely wrong. So by proving that the angles in a triangle cannot be anything greater than 180 degrees or less than 180 degrees and that 180 degrees works, we can state that all triangles have 180 degrees.

I think that this is somewhat correct. I hope it proves it.


At 11/22/2005 9:59 PM, Blogger Mr. Kuropatwa said...

I think a diagram is missing?

At 11/22/2005 10:03 PM, Blogger GraemeW said...

i think blogger is deviously working against me, because it won't upload my image and it doesn't like my preformatted text

At 11/22/2005 10:19 PM, Blogger GraemeW said...

nevermind blogger just doesn't like my mothers computer. The picture uploads just fine on a different computer.

At 11/22/2005 10:42 PM, Blogger Mr. Kuropatwa said...

Graeme, we know that a + b = d BECAUSE there are 180 degrees in a triangle -- you have to prove that fact before you can use it.

Nonetheless, I'm impressed with your effort -- you're the first person who has tried to prove it without looking it up on the internet. ;-)

At 11/25/2005 6:11 PM, Blogger GraemeW said...

Well is this correct now Mr. Kuropatwa?


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