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:

The awkwardness of the fifth postulate remained a blemish in a work that, otherwise, was of immortal perfection. We knew the geometry of space with certainty and Euclid had revealed it …

That, if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which …

Euclid's 5th postulate, also known as the parallel postulate, is an important part of geometry because it helps to define what it means for two lines to be parallel.

Besides 23 definitions and several implicit assumptions, Euclid derived much of the planar geometry from five postulates. A straight line may be drawn between any two points.

But it's Postulate 5—the famous parallel postulate—that stirs the greatest intrigue. It claims that if a line intersects two others and the interior angles on one side are less than two right angles, …

Study Euclids Fifth Postulate in Geometry with concepts, examples, videos and solutions. Make your child a Math Thinker, the Cuemath way. Access FREE Euclids Fifth Postulate Interactive …

Apr 24, 2016 · The solution to the problem of the fifth postulate (more precisely its removal) was obtained by a geometry created by N.I. Lobachevskii (1826) in which the fifth postulate does …

Dec 3, 2025 · Euclid's fifth postulate cannot be proven as a theorem, although this was attempted by many people. Euclid himself used only the first four postulates ("absolute geometry") for the …

His axioms and postulates are studied until now for a better understanding of the subject. In this article, you will be concentrating on the equivalent version of his 5th postulate given by John …