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Parallel postulate - Wikipedia

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In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's Elements, is a distinctive axiom in Euclidean geometry. It states that, in two-dimensional geometry: If a line segment intersects two straight lines forming two interior angles on the same side that are less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles. This postulate does not specifically talk about parallel lines;[1] it is only a postulate related to parallelism. Euclid gave the definition of parallel lines in Book I, Definition 23[2] just before the five postulates.[3] Euclidean geometry is the study of geometry that satisfies all of Euclid's axioms, including the parallel postulate. The postulate was long considered to be obvious or inevitable, but proofs were elusive. Eventually, it was discovered that inverting the postulate gave valid, albeit different geometries. A

Parallel postulate - Wikipedia Jump to content From Wikipedia, the free encyclopedia Geometric axiom If the sum of the interior angles α and β is less than 180°, the two straight lines, produced indefinitely, meet on that side. In geometry , the parallel postulate is the fifth postulate in Euclid's Elements and a distinctive axiom in Euclidean geometry . It states that, in two-dimensional geometry: If a straight line intersects two other straight lines forming two interior angles on the same side that are less than two right angles , then the two lines, if extended indefinitely, meet on that s

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