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Re: Fundamental and trivial question on triangle inequality.
Posted:
Sep 19, 2011 6:16 AM


If A>0, B>0, C>0, A+B>C, A+C>B, C+B>A then a triangle can be constructed with sides A, B, C. 1. AB<C<A+B Triangle Segment Range (?) 2. C>0 Deduction (The absolute value can only be a nonnegative integer) 3. C<A+B Statement 1 4. AC<B<A+C Triangle Segment Range (?) 5. B>0 Deduction (The absolute value can only be a nonnegative integer) 6. B<A+C Statement 4 7. BC<A<B+C Triangle Segment Range (?) 8. A>0 Deduction (The absolute value can only be a nonnegative integer) 9. A<B+C Statement 7 The given sides satisfy the triangle segment range because they can be derived from it. Therefore, the given segment conditions can form a triangle. QED
I think this is not quite clear. Ask me more if you did not understand.



