Comparison of Euclidean, spherical, and hyperbolic geometries

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Comparison of Euclidean, spherical, and hyperbolic geometries

Given a line and a point not on the line, there exist(s) ____________ through the given point

and parallel to the given line.

a) exactly one line (Euclidean)

b) no lines (spherical)

c) infinitely many lines (hyperbolic)

Euclid s fifth postulate is ____________.

a) true (Euclidean)

b) false (spherical)

c) false (hyperbolic)

The sum of the interior angles of a triangle ______ 180 degrees.

a) = (Euclidean)

b) > (spherical)

c) < (hyperbolic)

See as table:

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