Plane geometry—This includes common features such as circles, lines, triangles, and polygons.

Solid geometry—This also includes such figures as circles and lines, as well as polyhedrons.

Spherical geometry—This includes shapes such as spherical triangles (see below) and polygons.

There are other types of geometry, too, including projective geometry and non-Euclidean geometry. Most of these are more complex forms of geometry that each have their own special reasons for use.