Look at the construction below. Can you move the points in the construction so that segments a, b, and c form a triangle? In this exploration, you will determine the conditions required for side lengths to form triangles. This set of conditions is known as the Triangle Inequality Theorem.

Answer the following questions below. Use the construction above to help you if you want. [br][br]1) Set the side lengths a, b, and c to 7, 10, and 19, respectively. Can these three segments form a triangle? Why or why not?[br][br]2) Use the slider to adjust the length of side a only. As you do so, manipulate the points to try to form triangles. What is the smallest value of side a that will allow you to create a triangle? What is the largest value of side a that will allow you to create a triangle?[br][br]3) Experiment with the lengths of all three sides. What has to be true about the relationships between the sides in order to be able to form triangles?