Equilateral Triangles can't be obtuse w/ indirect reasoning

[blackbelt]

Q: Use indirect reasoning to show that an equilateral triangle cannot be an obtuse triangle.


I don't really know how to start and was looking for some help. Anybody got anything?

 

[stapel]

What is your book's definition of "indirect reasoning"? :?:

One place to start the proof might be with the definition of "equilateral" triangle. :wink:

Eliz.

P.S. Welcome to FreeMathHelp!

 

[pka]

There is a commonly theorem known that an equilateral triangle is also equiangular. But the sum of the measures of the angles of any triangle is \(\displaystyle \pi\). Any obtuse triangle has an angle greater that \(\displaystyle \pi/2\).

 

[blackbelt]

What is your book's definition of "indirect reasoning"? :?:

One place to start the proof might be with the definition of "equilateral" triangle. :wink:

Eliz.

P.S. Welcome to FreeMathHelp!

My book's definition is "a type of reasoning in which all possibilities are considered and than the unwanted ones are proved false. The remaining possibilities must be true."

Any suggestions?

 

[stapel]

What is your book's definition of "indirect reasoning"?

My book's definition is "a type of reasoning in which all possibilities are considered and than the unwanted ones are proved false. The remaining possibilities must be true." Any suggestions?

You have two cases: The triangle is obtuse (has one angle with a measure greater than ninety degrees) or it is not. You want to prove that it is not. So what does the definition of "indirect reasoning" tell you to assume?

Then, using the hint from the other tutor, where does this assumption lead? :wink:

Eliz.