Triangle inequalities refer to a set of mathematical inequalities that describe the relationships between the lengths of the sides of a triangle. The most fundamental triangle inequalities assert that for any triangle with side lengths \(a\), \(b\), and \(c\): 1. \(a + b > c\) (the sum of the lengths of any two sides must be greater than the length of the third side) 2. \(a + c > b\) 3.
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