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anonymous
 3 years ago
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.
anonymous
 3 years ago
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.

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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0if 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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Thank you very much that helped a lot :)

across
 3 years ago
Best ResponseYou've already chosen the best response.2I'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 \(a\to\infty\)?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I 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)

across
 3 years ago
Best ResponseYou've already chosen the best response.2Simplifying the problem,dw:1342802092805:dwwe 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?

across
 3 years ago
Best ResponseYou've already chosen the best response.2What if we also observe this in a nonEuclidean setting? Say, a sphere?dw:1342802292429:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Thank you I was looking for a contradiction :)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0@ParthKohli the angles of a triangle do not add up to 180 degrees in a spherical geometry!

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Think about it this way dw:1342802984980:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I 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.

across
 3 years ago
Best ResponseYou've already chosen the best response.2@sauravshakya, not without deformations.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Actually 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.
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