Parallel postulate

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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 side on which the angles sum to less than two right angles. This may be also formulated as: If a straight line intersects two other straight lines, the two interior angles on the same side add to less than two right angles if and only if the two lines, if extended indefinitely, meet on that side. The difference between the two formulations lies in the converse of the first formulation: If a straight line intersects two other straight lines that intersect on some side of first line, the two interior angles on this side add to less than two right angles. This latter assertion is proved in Euclid's Elements by using the...

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