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The hyperbolic parallel postulate states that given a line L and a point P, not on the line, there are at least two distinct lines through P that do not intersect L.The negation is that given a line L and a point P, not on the line, there is at most one line through P that does not intersect L.The negation includes the case where there is exactly one such line - which is the Euclidean space.
This is 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.
Any equation parallel to the x-axis is of the form:y = constant In this case, you can figure out the constant from the given point.
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The Playfair Axiom (or "Parallel Postulate")
Playfair Axiom
Assume there are no lines through a given point that is parallel to a given line or assume that there are many lines through a given point that are parallel to a given line. There exist a line l and a point P not on l such that either there is no line m parallel to l through P or there are two distinct lines m and n parallel to l through P.
Euclid's parallel postulate.
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infinitely many
Exactly one. No more and no less.
"Euclidean" geometry is the familiar "standard" geometry. Until the 19th century, it was simply "geometry". It features infinitely divisible space, up to three dimensions, and, most notably, the "parallel postulate": "Given a line, and a point not on the line, there is exactly one line that can be drawn through the point and parallel to the given line."
Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the given line (-7,3); x=4
Parallel straight line equations have the same slope but with different y intercepts
Finding the midpoint of a segment Drawing a perpendicular line segment from a given point to a given segment Drawing a perpendicular line segment through a given point on a given segment Drawing a line through a given point parallel to a given line
Finding the midpoint of a segment Drawing a perpendicular line segment from a given point to a given segment Drawing a perpendicular line segment through a given point on a given segment Drawing a line through a given point parallel to a given line