Plane geometry is that subsection of geometry that deals with figures in a two-dimensional plane. Euclidean geometry, sometimes called parabolic geometry, is divided into two subsections: plane geometry, geometry dealing with figures in a plane, and solid geometry, geometry dealing with solid in three-dimensional space. Plane geometry is sometimes called two-dimensional Euclidean geometry and deals with figures such as circles, lines, polygons and the like. Plane geometry is concerned with the study of figures in two-dimensional Euclidean space, which is usually denoted R², also known as the Euclidean plane. This branch of Euclidean geometry is also focused on studying the properties of flat surfaces.

Plane geometry is a branch of Euclidean geometry, developed by Greek mathematician Euclid in the 4th century B.C., that is governed by Euclid's five postulates as laid out in his work The Elements. In the early 20th century mathematicians recognized that...