Knowing all the different properties of lines and shapes is important. But if we're truly going to rule the world of geometry, we need to be the absolute overlords of it. We're talking about a level of omnipotence that makes the very universe quake with fear.
We need to know how to create constructions.
It might sound like we're hammering up drywall and fixing the plumbing, but knowing how to construct shapes is a crucial skill in the world of geometry. How else can you create, change, and destroy geometric shapes at will?
Constructions are helpful, too, especially when proofs seem to be going nowhere. The simple addition of a perpendicular or angle bisector might change a frustrating triangle problem into a much simpler proof than you may have realized. Cutting things in half often does that.
You don't need any fancy rulers, protractors, or high-tech computer algorithms to make these shapes, either. Just pick up an old-school straightedge and compass, and the geometric world is your oyster-shaped construction.