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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 many lines are parallel to a given line through a given point?
zero
how to negate the hyperbolic parallel postulate?
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.
If there is a line and a point not on the line then there is exactly lines trough the point parallel to the given line?
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.
What is the equation of a line that passes through the point 1 2 and is parallel to the x-axis?
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.
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")
Through a given point on a given line there is exactly one line parallel to the given line what does it define?
Playfair Axiom
What is another name for the Playfair Axiom?
Another name for the Playfair Axiom is the Euclid's Parallel Postulate. It states that given a line and a point not on that line, there is exactly one line parallel to the given line passing through the given 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.
Which conjecture justifies the construction of a line parallel to a given line through a given point?
Euclid's parallel postulate.
How many lines are parallel to a given line through a given point?
zero
In hyperbolic geometry how many lines are there parallel to a given line through a given point?
infinitely many
How many lines are parallel to a line through a point not on the line?
Exactly one. No more and no less.
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."
What is an equation in slope-intercept form for the line that passes through the given point and is 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
How do you write an equation that is parallel to a given line and passes through the given point?
Parallel straight line equations have the same slope but with different y intercepts
Constructions can be accomplished with paper folding?
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
