## Triangle Inequality Theorem Lesson

### What is the Triangle Inequality Theorem?

The triangle inequality theorem tells us that:

**The sum of two sides of a triangle must be greater than the third side.**

This theorem can be used to prove if a combination of three triangle side lengths is possible. See the image below for an illustration of the triangle inequality theorem.

INTRODUCING

### Triangle Inequality Theorem Example Problem

Referencing sides *x*, *y*, and *z* in the image from the above section, use the triangle inequality theorem to eliminate impossible triangle side length combinations from the following list.

- x = 2, y = 3, z = 5
- x = 5, y = 12, z = 13
- x = 3, y = 4, z = 5
- x = 12, y = 13, z = 27
- x = 2, y = 9, z = 12

Solution:

**Side length combinations #1, #4, and #5 do not satisfy the requirements of the triangle inequality theorem and therefore are not possible.**