# The Triangle Inequality

The Triangle Inequality

The triangle inequality is usually expressed algebraically using vectors in two dimensions. This Demonstration shows two vectors, and , and their sum . These three vectors form a triangle unless is a multiple of . The triangle inequality states that the sum of the lengths of two sides of a triangle is at least as large as the length of the third side. In symbols, .

x

y

x+y

x

y

|x|+|y|≥|x+y|