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If we are given the lengths of the three sides of a triangle, and we simply add the 2 smallest sides and check to see if the sum is larger than the third side, will this always yield the correct answer i.e. will it always tell us if the triangle is a viable one? Thanks.

Joebevo
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    Yes.I think this is proved in geometry: any three positive real numbers in which the sum of any two is greater than the third one are the sides of a triangle that is constructible. – DonAntonio Aug 29 '13 at 10:25
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    Actually, I think its the easiest way to construct a triangle: Given three lengths $a,b,c$ first draw a chord of length $a$, at the first endpoint draw a circle of radius $b$ and at the second endpoint a circle of radius $c$. These two circles must intersect, because the distance of their centers $O_1O_2=a$ is less than the sum of radii $b+c$. Let $X$ be a point of intersection, then the triangle $\triangle O_1O_2X$ has side lengths $a,b,c$. – walcher Aug 29 '13 at 10:31

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