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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:
parallel postulate, One of the five postulates, or axioms, of Euclid underpinning Euclidean geometry. It states that through any given point not on a line there passes exactly one line parallel to that line in the same plane.
The meaning of PARALLEL POSTULATE is a postulate in geometry: if a straight line incident on two straight lines make the sum of the angles within and on the same side less than two right angles the two straight lines being produced indefinitely meet one another on whichever side the two angles are less than the two right angles —called also ...
Parallel Postulate. Given any straight line and a point not on it, there "exists one and only one straight line which passes" through that point and never intersects the first line, no matter how far they are extended.
Parallel postulate definition: If a line segment crosses two lines such that the measure of their inner angles on the same side is less than two right angles when added together,...
The parallel postulate is a fundamental principle in Euclidean geometry that states that through any point not on a given line, there exists exactly one line parallel to the given line.
The parallel postulate is a fundamental principle in Euclidean geometry stating that through any given point not on a line, there is exactly one line parallel to the original line.
For over two millenia mathematicians tried to prove Euclid's parallel postulate from the other four of his postulates. This was known early on to be a useless effort, but it was not known until the 19th century why they were right.
The parallel postulate tells us that if the two labeled angles don't add up to exactly 180° in measure, the two lines u and v aren't parallel. One of the labeled angles is 100° and the other is a right angle (or 90°).
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. In Euclidean geometry, two lines are parallel if they never intersect, no matter how far they are extended.