The Triangle Inequality is a theorem that simply states that the sum of the lengths of any to sides of a triangle \(a\) and \(b\) must be greater than or equal to the final side \(c\). Formally,

\[c \leq a + b\]

The above is valid in Euclidean Space but there is a different generalization of the theorem for other types of geometries. The Triangle Inequality in these spaces is a theorem about distances, and it written using vectors and their norms.

\[||x + y|| \leq ||x|| + ||y||\]