# Triangle Inequality Theorem

- Author:
- William Rodgers

This theorem is extremely important but very easy to see. Instead of looking at the measure of the angles, you will look at the length of sides. As you investigate this theorem, be sure to look at all sorts of triangles (equilateral, right, acute, and obtuse). Here's what I want you to do: As you change triangle ABC, choose any two sides of the triangle to add together. What do you notice about their sum in comparison to the other side of the triangle? Is this always the case? Is it possible to find an instance where this doesn't happen? Explore some different triangles and see what you can conclude.

Which statement matches the discovery you made concerning the lengths of the sides of triangles?

You may need to go back to the top to examine a few triangles before you fill in the blank to this statement accurately. The shortest side of any triangle will always be across from the _____________ angle of that triangle.