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GeometryPleaseHelp
Prove the following theorem indirectly. We will give you a start. Prove that a triangle cannot have two right angles. A triangle cannot have two right angles. Suppose a triangle had two right angles.
if a triangle will have two right angles then the two sides of the triangle will be parallel to each other And if two sides of a triangle will be parallel to each other than it will not be a triangle.|dw:1342801549724:dw|
Thank you very much that helped a lot :)
I'm sorry to hijack your question, but this exercise brings up an interesting case study: Given the following isosceles triangle, |dw:1342801703803:dw| what is the limit of \(\theta\) as \(a\to\infty\)?
I still really don't know what it means, I need a statement to make a theorem indirect and that is how the question was stated, it is really confusing to me x)
Simplifying the problem,|dw:1342802092805:dw|we are left to compute\[\theta=\cos^{-1}\left(\lim_{a\to\infty}\frac{b}{a}\right)=90.\]The question is, however, is this still a triangle?
What if we also observe this in a non-Euclidean setting? Say, a sphere?|dw:1342802292429:dw|
Thank you I was looking for a contradiction :)
@ParthKohli the angles of a triangle do not add up to 180 degrees in a spherical geometry!
Think about it this way |dw:1342802984980:dw|
I think it add up to 180 degree because u can draw a triangle in a plane paper and roll it to make a cylinder which surface has a triangle.
@sauravshakya, not without deformations.
Actually I think you may need that third the angle < 180\(^o\) in spherical geometry. @across is correct, you have to have the paper stretch or tear to make it work. And it's got wrinkles everywhere.