Lambert quadrilateral
In hyperbolic geometry, a Lambert quadrilateral is a quadrilateral^{} with exactly three right angles^{}. Since the angle sum of a triangle in hyperbolic geometry is strictly less than $\pi $ radians, the angle sum of a quadrilateral in hyperbolic geometry is strictly less than $2\pi $ radians. Thus, in any Lambert quadrilateral, the angle that is not a right angle must be acute.
The discovery of Lambert quadrilaterals is attributed to Johann Lambert.
Both pairs of opposite sides of a Lambert quadrilateral are disjointly parallel since, in both cases, they have a common perpendicular^{}. Therefore, Lambert quadrilaterals are parallelograms^{}. Note also that Lambert quadrilaterals are right trapezoids^{}.
Below are some examples of Lambert quadrilaterals in various models. In each example, the Lambert quadrilateral is labelled as $ABCD$.

•
The BeltramiKlein model:
In each of these examples, blue lines indicate verification of right angles by using the poles, and green lines indicate verification of acute angles by using the poles. (Recall that most other models of hyperbolic geometry are angle preserving. Thus, verification of angle measures is unnecessary in those models.)

•
The Poincaré disc model:

•
Title  Lambert quadrilateral 

Canonical name  LambertQuadrilateral 
Date of creation  20130322 17:08:04 
Last modified on  20130322 17:08:04 
Owner  Wkbj79 (1863) 
Last modified by  Wkbj79 (1863) 
Numerical id  24 
Author  Wkbj79 (1863) 
Entry type  Definition 
Classification  msc 51M10 
Classification  msc 5100 
Synonym  Lambert’s quadrilateral 
Related topic  RightTrapezoid 