The part of geometry which studies two-dimensional figures drawn on a flat surface is known as plane geometry. This knowledge is very important because many problems people attempt to solve in everyday life are either two-dimensional by nature, or they can be simplified into two dimensions.

Many problems might appear to be three-dimensional at first glance, but they are actually two-dimensional. One such example is a stream of water coming out of a stationary garden hose or a fire hose. This is because the water is always on a plane - a vertical plane. The elimination of the third dimension makes it much easier to study the projectile motion.

Although many problems are truly three-dimensional, we may simplify them into two-dimensional problems to make a solution easier, if we can do that with reasonable accuracy. For example, plane surveys always treat any small segment of land as a horizontal plane.

When observing nature closely, we find that the seemingly unusual and complicated shapes are merely extensions of a few simple basic figures. In plane geometry, these simple basic shapes include point, line, triangle, quadrilateral, many-sided polygons, and circle. Each has a distinct character of its own. When combined to form a unique object, new properties and useful applications are formed.