# Category:Examples of Triangle Inequality

This category contains examples of use of Triangle Inequality.

### Geometry

Given a triangle $ABC$, the sum of the lengths of any two sides of the triangle is greater than the length of the third side.

In the words of Euclid:

In any triangle two sides taken together in any manner are greater than the remaining one.

### Real Numbers

Let $x, y \in \R$ be real numbers.

Let $\size x$ denote the absolute value of $x$.

Then:

$\size {x + y} \le \size x + \size y$

### Complex Numbers

Let $z_1, z_2 \in \C$ be complex numbers.

Let $\cmod z$ denote the modulus of $z$.

Then:

$\cmod {z_1 + z_2} \le \cmod {z_1} + \cmod {z_2}$

## Pages in category "Examples of Triangle Inequality"

The following 6 pages are in this category, out of 6 total.