Editing Non-Euclidean geometry (section)

==Uncommon properties==
[[File:Lambert quadrilateral.svg|upright|thumb|left|{{center|Lambert quadrilateral in hyperbolic geometry}}]]
[[File:Saccheri quads.svg|150px|thumb|{{center|Saccheri quadrilaterals in the three geometries}}]]

Euclidean and non-Euclidean geometries naturally have many similar properties, namely those that do not depend upon the nature of parallelism. This commonality is the subject of [[absolute geometry]] (also called ''neutral geometry''). However, the properties that distinguish one geometry from others have historically received the most attention.

Besides the behavior of lines with respect to a common perpendicular, mentioned in the introduction, we also have the following:
* A [[Lambert quadrilateral]] is a quadrilateral with three right angles. The fourth angle of a Lambert quadrilateral is [[Acute angle|acute]] if the geometry is hyperbolic, a [[right angle]] if the geometry is Euclidean or [[Obtuse angle|obtuse]] if the geometry is elliptic. Consequently, [[rectangle]]s exist (a statement equivalent to the parallel postulate) only in Euclidean geometry.
* A [[Saccheri quadrilateral]] is a quadrilateral with two sides of equal length, both perpendicular to a side called the ''base''. The other two angles of a Saccheri quadrilateral are called the ''summit angles'' and they have equal measure. The summit angles of a Saccheri quadrilateral are acute if the geometry is hyperbolic, right angles if the geometry is Euclidean and obtuse angles if the geometry is elliptic.
* The sum of the measures of the angles of any triangle is less than 180° if the geometry is hyperbolic, equal to 180° if the geometry is Euclidean, and greater than 180° if the geometry is elliptic. The ''defect'' of a triangle is the numerical value (180° &minus; sum of the measures of the angles of the triangle). This result may also be stated as: the defect of triangles in hyperbolic geometry is positive, the defect of triangles in Euclidean geometry is zero, and the defect of triangles in elliptic geometry is negative.