# Triangle Inequality

Topic:
Geometry
Slide for different distances. We are trying to find what values can create triangles and which cannot. When you are finished you should have a concept of the Triangle Inequality Theorem.
What values give a triangle, which don't don't? Do the following: Leave AB=5 and BC=3 Slide AC smaller. When does the triangle disappear? Slide AC larger. When does the triangle disappear? Make AB=7, BC=3 and AC=5 Slide AC smaller and then larger. The two times the triangles disappears? Make AB=3, BC=5 and AC=6 Slide BC smaller and then larger. The two times the triangles disappears? Make AB=4, BC=2.5 and AC=6 Slide AB smaller and then larger. The two times the triangles disappears? Make AB=6.4, BC=2.7 and AC=6 Slide AC smaller and then larger. The two times the triangles disappears? What must be true for a triangle to exist? If you are given three different lengths, how can you tell if you can create a triangle with those lengths? If I give you two different lengths, how can you determine the possible lengths of the missing side of a triangle? Write about your conjectures you have for the previous questions and why you think it is true. If it helps, consider your audience to be a student in this class who is going to be absent this week.