# Triangle Inequality

- Author:
- Eric Fitton

- 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.