22+ The Triangle Inequality Theorem
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. Theorem 38 (triangle inequality theorem): Any side of a triangle must be shorter than the other two sides added together.

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This set of conditions is known as the triangle inequality theorem. The triangle inequality theorem states that any side of a triangle is always shorter than the sum of the other two sides. The sum of the lengths of any two sides of a triangle is greater than the third side.

In other words you can not construct a triangle.

The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Triangle inequality theorem suggests that one side of a triangle must be shorter than the other two. Let $\cmod z$ be the modulus of $z$. Most norms instead satisfy the stronger ultrametric triangle inequality which says that.

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