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Which conjecture justifies the construction of a line parallel to a given line through a given point?
Euclid's parallel postulate.
Through a point not on the line exactly one line can be drawn parallel to the?
... given line. This is one version of Euclid's fifth postulate, also known as the Parallel Postulate. It is quite possible to construct consistent systems of geometry where this postulate is negated - either many parallel lines or none.
What are the names of Non-Euclidean Geometries?
Answer The two commonly mentioned non-Euclidean geometries are hyperbolic geometry and elliptic geometry. If one takes "non-Euclidean geometry" to mean a geometry satisfying all of Euclid's postulates but the parallel postulate, these are the two possible geometries.
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.
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.
