Illustrate Theorem on Triangle Inequality Qtr4_M1

Illustrate Theorem on Triangle Inequality Qtr4_M1

The Triangle Inequality Theorem states that the lengths of any two sides of a triangle sum to a length greater than the third leg. This gives us the ability to predict how long a third side of a triangle could be, given the lengths of the other two sides.

Example: Two sides of a triangle have measures 9 and 11. Find the possible range for the third side.

Solution: Let’s call the third side x

x. Then, by the triangle inequality theorem, we have the following three true statements.