Parallel postulate

In geometry, the parallel postulate, also called Euclid's fifth postulate since it is the fifth postulate in Euclid's Elements, is a distinctive axiom in what is now called Euclidean geometry. It states:

Related Topics:
Geometry - Euclid - Euclid's Elements - Axiom - Euclidean geometry

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If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which are the angles less than the two right angles.

Related Topics:
Line segment - Lines - Right angle

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Euclidean geometry is the study of geometry that satisfies all of Euclid's axioms, including the parallel postulate. A geometry where the parallel postulate is violated is known as a non-Euclidean geometry. Geometry that is independent of Euclid's fifth postulate (i.e., only assumes the first four postulates) is known as absolute geometry.

Related Topics:
Non-Euclidean geometry - Absolute geometry

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