section_path: Properties/Inequality
section_name: Inequality
paragraph_text: Inequality
  
  The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side. A triangle with three given positive side lengths exists if and only if those side lengths satisfy the triangle inequality. The sum of two side lengths can equal the length of the third side only in the case of a degenerate triangle, one with collinear vertices.