Pronunciation: /dʒiˈɒ mɪ tri/ ?

Geometry is the study of points, lines, and shapes in space1. Each branch of geometry is defined by the basic assumptions, or axioms, of that geometry. All other properties and theorems are derived from these basic assumptions.

Euclidean geometry has five basic assumptions or axioms:

  1. Any two points can be joined by a straight line.
  2. Any straight line segment can be extended indefinitely in a straight line.
  3. Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center.
  4. All right angles are congruent.
  5. If two lines intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough.
For more information on the axioms of Euclidean Geometry, see Elements Book I by Euclid. Translated by D. Joyce.

Plane geometry is the study of objects in a 2-dimensional space. Solid geometry is the study of objects in a 3-dimensional space.


  1. geometry. WordNet. Princeton University. (Accessed: 2011-01-08).
  2. Keller, Samuel Smith. Mathematics for Engineering Students, Plane and Solid Geometry, pg 1. D. Van Nostrand Company, 1908. (Accessed: 2010-01-02).
  3. Casey, John, LL.D., F.R.S.. The First Six Books of the Elements of Euclid, Introduction. Casey, John, LL.D. F.R.S.. Hodges, Figgis & Co., 1890. (Accessed: 2010-01-02).
  4. Descartes, René. La géométrie. A. Hermann, Librarie Scientifique, 1886. (Accessed: 2010-01-14).

More Information

  • Euclid. Elements. 2009-03-12. D. Joyce.

Educator Resources

  • Surveying and Geometry. NASA Connect. NASA LaRC Office of Education. 2010-02-18.
  • Surveying and Studying Mars. NASA Connect. NASA LaRC Office of Education. 2010-02-18.
  • Pythagoras Theorem and Ellipses. NASA Connect. NASA LaRC Office of Education. 2010-02-18.

Cite this article as:

Geometry. 2009-12-15. All Math Words Encyclopedia. Life is a Story Problem LLC.


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Revision History

2009-12-15: Added "References" (McAdams, David.)
2008-08-04: Added More Information. Added reference to Elements, vocabulary links (McAdams, David.)
2007-07-12: Initial version (McAdams, David.)

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