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How many lines can be drawn passing through two given line?
Through two given lines, there can be either zero, one, or infinitely many lines that can be drawn, depending on their relationship. If the two lines are parallel, no line can pass through both. If they intersect, exactly one line can be drawn through their intersection point. If they are coincident (the same line), then infinitely many lines can be drawn through them.
In Euclidean geometry if there is a line and a point not on the line then there is exactly one line through the point and the parallel to the given line. True or false?
True. In Euclidean geometry, if there is a line and a point not on that line, there exists exactly one line that can be drawn through the point that is parallel to the given line. This is known as the Parallel Postulate, which states that for a given line and a point not on it, there is one and only one line parallel to the given line that passes through the point.
What does the following Define through a given point not a given line there is exactly one line parallel to the given line?
The statement means that through any point not located on a given line, there is exactly one line that can be drawn that is parallel to the original line. This is a fundamental concept in Euclidean geometry, often referred to as the Parallel Postulate. It asserts that the parallel line will never intersect the given line, maintaining a constant distance apart from it. This principle underlies many geometric constructions and proofs.
Is it possible to construct a line that is parallel to any given line and that passes through a point that is not on the given line?
Yes. That's always possible, but there's only one of them.
How many lines are parallel to a given line through a given point?
zero
How many lines can be drawn passing through two given line?
Through two given lines, there can be either zero, one, or infinitely many lines that can be drawn, depending on their relationship. If the two lines are parallel, no line can pass through both. If they intersect, exactly one line can be drawn through their intersection point. If they are coincident (the same line), then infinitely many lines can be drawn through them.
In Euclidean geometry if there is a line and a point not on the line then there is exactly one line through the point and the parallel to the given line. True or false?
True. In Euclidean geometry, if there is a line and a point not on that line, there exists exactly one line that can be drawn through the point that is parallel to the given line. This is known as the Parallel Postulate, which states that for a given line and a point not on it, there is one and only one line parallel to the given line that passes through the point.
How do you negate the euclidean parallel postulate?
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.
What postulate is not of euclidean geometry?
Euclidean Geometry is based on the premise that through any point there is only one line that can be drawn parallel to another line. It is based on the geometry of the Plane. There are basically two answers to your question: (i) Through any point there are NO lines that can be drawn parallel to a given line (e.g. the geometry on the Earth's surface, where a line is defined as a great circle. (Elliptic Geometry) (ii) Through any point, there is an INFINITE number of lines that can be drawn parallel of a given line. (I think this is referred to as Riemannian Geometry, but someone else needs to advise us on this) Both of these are fascinating topics to study.
A given line is always parallel to itself?
False.
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")
Is it possible to construct a line that is parallel to any given line and that passes through a point that is not on the given line?
Yes. That's always possible, but there's only one of them.
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.
How many lines are parallel to a given line through a given point?
zero
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 eullidean geometry?
"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."
