1. the geometry of 2-dimensional figures;

The Collaborative International Dictionary of English v.0.48:

Plane \Plane\, a. [L. planus: cf. F. plan. See Plan, a.] Without elevations or depressions; even; level; flat; lying in, or constituting, a plane; as, a plane surface. [1913 Webster] Note: In science, this word (instead of plain) is almost exclusively used to designate a flat or level surface. [1913 Webster] Plane angle, the angle included between two straight lines in a plane. Plane chart, Plane curve. See under Chart and Curve. Plane figure, a figure all points of which lie in the same plane. If bounded by straight lines it is a rectilinear plane figure, if by curved lines it is a curvilinear plane figure. Plane geometry, that part of geometry which treats of the relations and properties of plane figures. Plane problem, a problem which can be solved geometrically by the aid of the right line and circle only. Plane sailing (Naut.), the method of computing a ship's place and course on the supposition that the earth's surface is a plane. Plane scale (Naut.), a scale for the use of navigators, on which are graduated chords, sines, tangents, secants, rhumbs, geographical miles, etc. Plane surveying, surveying in which the curvature of the earth is disregarded; ordinary field and topographical surveying of tracts of moderate extent. Plane table, an instrument used for plotting the lines of a survey on paper in the field. Plane trigonometry, the branch of trigonometry in which its principles are applied to plane triangles. [1913 Webster]WordNet (r) 3.0 (2006):

plane geometry n 1: the geometry of 2-dimensional figures