Summary of Geometries
Euclidean, Hyperbolic, and Elliptic Geometries
Euclidean  Hyperbolic  Elliptic  

Triangles  Angles must sum to exactly 180 degrees

Angles must sum to less that 180 degrees

Angles must sum to greater 180 degrees

Parallel Lines  There is only one line that is parallel to line l and passes through a point P

There are infinitely many lines that are parallel to line l and pass through a point P  There is no line that is parallel to line l and passes through a point P 