State Playfair's axiom .
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given a line m and a point p, there exists a unique line l passing through p parallel to m.
two distinct intersecting lines cannot be parallel to the same line.
two distinct intersecting lines cannot be parallel to the same line.
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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.
It is equivalent to Euclid's parallel postulate in the context of Euclidean Geometry and was named after the Scottish mathematician John Playfair. The statement is often written with the phrase, "there is one and only one parallel".
It is equivalent to Euclid's parallel postulate in the context of Euclidean Geometry and was named after the Scottish mathematician John Playfair. The statement is often written with the phrase, "there is one and only one parallel".
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