10 Distinct Triangles in a star

Cauchy Schwarz vs Triangle Inequality

Triangle Inequality vs Cauchy Schwarz

Triangle Inequality n dimensional Proof

Note to prove this we need to use Cauchy Schwarz Inequality. Also notice that triangle inequality is addition. In short: Triangle inequality says the sum of two sides is bigger than 3rd side. Cauchy inequality says the product of two sides is bigger than their dot product

Triangle and Reverse Triangle Inequality Proof