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That portion of Geometry dealing with figures in a Plane, as opposed to Solid Geometry. Plane geometry deals with the Circle, Line, Polygon, etc.
See also Constructible Polygon, Geometric Construction, Geometry, Solid Geometry, Spherical Geometry
References
Altshiller-Court, N.  College Geometry: A Second Course in Plane Geometry for Colleges and Normal Schools, 2nd ed.,
  rev. enl.  New York: Barnes and Noble, 1952.
 
Casey, J.  A Treatise on the Analytical Geometry of the Point, Line, Circle, and Conic Sections,
  Containing an Account of Its Most Recent Extensions with Numerous Examples, 2nd rev. enl. ed.
  Dublin: Hodges, Figgis, & Co., 1893.
 
Coxeter, H. S. M. and Greitzer, S. L.
  Geometry Revisited.  Washington, DC: Math. Assoc. Amer., 1967.
 
Coxeter, H. S. M.  Introduction to Geometry, 2nd ed.  New York: Wiley, 1969.
 
Dixon, R.  Mathographics.  New York: Dover, 1991.
 
Gallatly, W.  The Modern Geometry of the Triangle, 2nd ed.  London: Hodgson, 1913.
 
Heath, T. L.  The Thirteen Books of the Elements, 2nd ed., Vol. 1: Books I and II.  New York: Dover, 1956.
 
Heath, T. L.  The Thirteen Books of the Elements, 2nd ed., Vol. 2: Books III-IX.  New York: Dover, 1956.
 
Heath, T. L.  The Thirteen Books of the Elements, 2nd ed., Vol. 3: Books X-XIII.  New York: Dover, 1956.
 
Hilbert, D.  The Foundations of Geometry.  Chicago, IL: Open Court, 1980.
 
Hilbert, D. and Cohn-Vossen, S.  Geometry and the Imagination.  New York: Chelsea, 1952.
 
Honsberger, R.  Episodes in Nineteenth and Twentieth Century Euclidean Geometry.  Washington, DC: Math. Assoc. Amer., 1995.
 
Johnson, R. A.  Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle.
  Boston, MA: Houghton Mifflin, 1929.
 
Kimberling, C.  ``Triangle Centers and Central Triangles.''  Congr. Numer. 129, 1-295, 1998.
 
Klee, V.  ``Some Unsolved Problems in Plane Geometry.''  Math. Mag. 52, 131-145, 1979.
 
Klee, V. and Wagon, S.  Old and New Unsolved Problems in Plane Geometry and Number Theory, rev. ed.
  Washington, DC: Math. Assoc. Amer., 1991.
 
Pedoe, D.  Circles: A Mathematical View, rev. ed.  Washington, DC: Math. Assoc. Amer., 1995.
 
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© 1996-9 Eric W. Weisstein