anonymous
  • anonymous
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.
Mathematics
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anonymous
  • anonymous
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.
Mathematics
jamiebookeater
  • jamiebookeater
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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anonymous
  • anonymous
Well...let's look at our options..
anonymous
  • anonymous
For A all of the angles would have to be acute...which automatically isnt a theorem...so we can cancel that out.
anonymous
  • 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
  • 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
  • anonymous
So the only possible option, and the easiest would be D. That it only has one obtuse angle.
pythagoras123
  • 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
  • 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
  • anonymous
yea that makes sense to me
anonymous
  • 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
  • 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
  • anonymous
exactly joe! thats I said first
anonymous
  • anonymous
Oh, Joe is right...so it would be B becuase it's the opposite of the right statement of D.
anonymous
  • anonymous
I forgot it was proof contradictory:)
anonymous
  • anonymous
Thanks guys! I got a 90

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