Tricky Triangles

Can you have triangles of different lengths? For example, can you have side lengths of:

1. 1, 2, 2
2. 1, 2, 3
3. 1, 2, 6
4. 2, 3, 4
5. 2, 3, 7
6. 3, 5, 7
7. 3, 5, 9

What generalizations can you make about the relationships of side lengths of triangles?

Extension:
Constructing Triangles: Construct triangles with particular attributes.