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Earn +20 ptsQ: Why is the parallel axiom in Euclid's geometry false in non-Euclidian geometry?
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Are two lines that are parallel to the same line parallel to each other?
Yes they are. It is delineated in something called the parallel postulate, and the axiom is also called Euclid's fifth postulate. This is boilerplate Euclidean geometry, and a link can be found below if you'd like to review the particulars.
Through a given point not on a given line there is exactly one line parallel to the given line?
The Playfair Axiom (or "Parallel Postulate")
A statement we accept as true without proof is a?
it is called an axiom
Who restated Euclid's 5th postulate?
Probably the best known equivalent of Euclid's parallel postulate, contingent on his other postulates, is Playfair's axiom, named after the Scottish mathematician John Playfair, which states:In a plane, given a line and a point not on it, at most one line parallel to the given line can be drawn through the point.
What is a statement that is accepted as truw without proof?
axiom
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