Triangles: Angle Sums

Date: 05/15/2002 at 19:30:08
From: Jack
Subject: triangle

Can you draw a triangle in which the sum of any two angles - no matter
which two you pick - is always less than 120 degrees?  Explain how you
can, or why you can't.

Date: 05/16/2002 at 05:34:49
From: Doctor Floor
Subject: Re: triangle

Hi, Jack,

Thanks for your question.

Suppose that in a triangle ABC we have

  <A + <B < 120 deg
  <B + <C < 120 deg
  <A + <C < 120 deg

then, if we add the three inequalities, we would have

  2*(<A + <B + <C) < 360 deg

and thus

 <A + <B + <C < 180 deg

and that is impossible. This proves that you cannot draw such a 
triangle.

Best regards,

- Doctor Floor, The Math Forum
  http://mathforum.org/dr.math/