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In a geometry class, the students were asked to prove the theorem below by contradiction.
Theorem: A triangle has at the most one obtuse angle.
Heather begins the proof with an assumption. Which statement will she most likely use as an assumption?
Let each angle of a triangle be acute.
Let two angles of a triangle be obtuse.
Let two angles of a triangle be right.
Let only one angle of a triangle be obtuse.
 2 years ago
 2 years ago
In a geometry class, the students were asked to prove the theorem below by contradiction. Theorem: A triangle has at the most one obtuse angle. Heather begins the proof with an assumption. Which statement will she most likely use as an assumption? Let each angle of a triangle be acute. Let two angles of a triangle be obtuse. Let two angles of a triangle be right. Let only one angle of a triangle be obtuse.
 2 years ago
 2 years ago

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Rain4meBest ResponseYou've already chosen the best response.1
Well...let's look at our options..
 2 years ago

Rain4meBest ResponseYou've already chosen the best response.1
For A all of the angles would have to be acute...which automatically isnt a theorem...so we can cancel that out.
 2 years ago

Qwerty90Best ResponseYou've already chosen the best response.1
Yes. I said the 2nd one because if the first assumption was that the triangle has more than one obtuse angle then it could be 2 obtuse. (the assumption is the contradiction)
 2 years ago

Rain4meBest ResponseYou've already chosen the best response.1
Right...but the second assumption is possible either... because if even one angle was obtuse, the other two must be acute's for it to actually be a triangle..
 2 years ago

Rain4meBest ResponseYou've already chosen the best response.1
So the only possible option, and the easiest would be D. That it only has one obtuse angle.
 2 years ago

pythagoras123Best ResponseYou've already chosen the best response.0
You can also prove it by taking the extreme case: Let the obtuse angle in the triangle be 91 degrees, the minimum requirement for an angle to be obtuse. 18091 = 89 An angle of 89 degrees is not an obtuse angle. Hence any triangle can only have one obtuse angle.
 2 years ago

Rain4meBest ResponseYou've already chosen the best response.1
It's not possible for a triangle to have more than one obtuse angle...or it wouldnt be a triangle...So the answer is D:)
 2 years ago

Qwerty90Best ResponseYou've already chosen the best response.1
yea that makes sense to me
 2 years ago

joemath314159Best ResponseYou've already chosen the best response.3
the fact that its not possible for a triangle to have 2 obtuse angles is why B is the correct answer for this problem. You are doing a proof by contradiction, which means you start with a contradictory statement.
 2 years ago

joemath314159Best ResponseYou've already chosen the best response.3
You are trying to prove that triangles can only have at most one obtuse angle, so you assume there are more than one, and force a contradiction.
 2 years ago

Qwerty90Best ResponseYou've already chosen the best response.1
exactly joe! thats I said first
 2 years ago

Rain4meBest ResponseYou've already chosen the best response.1
Oh, Joe is right...so it would be B becuase it's the opposite of the right statement of D.
 2 years ago

Rain4meBest ResponseYou've already chosen the best response.1
I forgot it was proof contradictory:)
 2 years ago

Qwerty90Best ResponseYou've already chosen the best response.1
Thanks guys! I got a 90
 2 years ago
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