## Qwerty90 3 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.

1. Rain4me

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

2. Rain4me

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

3. Qwerty90

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)

4. Rain4me

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..

5. Rain4me

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

6. 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.

7. Rain4me

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:)

8. Qwerty90

yea that makes sense to me

9. joemath314159

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.

10. joemath314159

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.

11. Qwerty90

exactly joe! thats I said first

12. Rain4me

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

13. Rain4me

I forgot it was proof contradictory:)

14. Qwerty90

Thanks guys! I got a 90