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Qwerty90 Group Title

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
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  1. Rain4me Group Title
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    Well...let's look at our options..

    • 2 years ago
  2. Rain4me Group Title
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    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
  3. Qwerty90 Group Title
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    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
  4. Rain4me Group Title
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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..

    • 2 years ago
  5. Rain4me Group Title
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    So the only possible option, and the easiest would be D. That it only has one obtuse angle.

    • 2 years ago
  6. pythagoras123 Group Title
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    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.

    • 2 years ago
  7. Rain4me Group Title
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    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
  8. Qwerty90 Group Title
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    yea that makes sense to me

    • 2 years ago
  9. joemath314159 Group Title
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    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
  10. joemath314159 Group Title
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    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
  11. Qwerty90 Group Title
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    exactly joe! thats I said first

    • 2 years ago
  12. Rain4me Group Title
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    Oh, Joe is right...so it would be B becuase it's the opposite of the right statement of D.

    • 2 years ago
  13. Rain4me Group Title
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    I forgot it was proof contradictory:)

    • 2 years ago
  14. Qwerty90 Group Title
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    Thanks guys! I got a 90

    • 2 years ago
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