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.
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Well...let's look at our options..
For A all of the angles would have to be acute...which automatically isnt a theorem...so we can cancel that out.
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)
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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..
So the only possible option, and the easiest would be D.
That it only has one obtuse angle.
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.
180-91 = 89
An angle of 89 degrees is not an obtuse angle.
Hence any triangle can only have one obtuse angle.
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:)
yea that makes sense to me
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.
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.
exactly joe! thats I said first
Oh, Joe is right...so it would be B becuase it's the opposite of the right statement of D.