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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- anonymous

- jamiebookeater

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- anonymous

Well...let's look at our options..

- anonymous

For A all of the angles would have to be acute...which automatically isnt a theorem...so we can cancel that out.

- anonymous

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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- anonymous

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..

- anonymous

So the only possible option, and the easiest would be D.
That it only has one obtuse angle.

- pythagoras123

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.

- anonymous

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:)

- anonymous

yea that makes sense to me

- anonymous

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.

- anonymous

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.

- anonymous

exactly joe! thats I said first

- anonymous

Oh, Joe is right...so it would be B becuase it's the opposite of the right statement of D.

- anonymous

I forgot it was proof contradictory:)

- anonymous

Thanks guys! I got a 90

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