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