# Triangle Inequality Theorem

- Author:
- William Gripentrog

## Question 1

In this triangle, the side lengths are given. In the left column on the bottom, you will notice that sides a & b have been added together. Move the vertices around and have the sum of sides a & b equal the length of side c. What happened when you attempted to complete this task?

Can you make a + b < c?

## Question 2

Generalize what you have discovered. If you are given three segment lengths, how can you tell if they form a triangle?

Can a triangle be formed if the lengths of three segments are 7, 10, & 19?

Can you form a triangle if the lengths of the segments are 2.3, 3.1, & 4.6?

Can a triangle be formed if the lengths of the segments of the triangle are n + 6, n^{2} -1, and 3n if n = 4?