Summary of Geometries

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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
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