Two figures are congruent if you can go from one to another through some combination of translations, reflections and rotations. In this tutorial, we'll really internalize this by working through the actual transformations.
Triangle congruence is not only useful when working with triangles, it's also useful with any other kind of polygon! Prove a few theorems about the properties of parallelograms using triangle congruence.
With just a compass and a straightedge (or virtual versions of them), you'll be amazed by how many geometric shapes you can construct perfectly. This tutorial gets you started with the building block of how to bisect angle and lines (and how to construct perpendicular bisectors of lines).