Triangles: Angle SumsDate: 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/ |
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