Triangle inequality

Property of geometry, also used to generalize the notion of "distance" in metric spaces

In mathematics, the triangle inequality states that for any triangle in Euclidean space, the sum of the lengths of any two sides must be greater than or equal to the length of the third side. If a, b, and c are the lengths of the sides of a triangle then: c ≤ a + b . {\displaystyle c\leq a+b.} The same inequality holds when the sides of the triangle are relabeled, so also ⁠ b ≤ a + c {\displaystyle b\leq a+c} ⁠ and ⁠ a ≤ b + c {\displaystyle a\leq b+c} ⁠.

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