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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.
Can a given point be in two lines?
A point has an infinite amount of lines passing through it.
Do lines that aren't parallel always intersect?
Yes, they do. By definition, lines that never intersect must be parallel, so all non-parallel lines must intersect at some point. Given that they are normal lines (y=mx+b) they will always have a point that suffices the equation when they are set equal to each other.
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 parallel lines intersect?
Parallel lines in the Euclidean plane do not intersect but all parallel lines in the projective plane intersect at the point at infinity.
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.
In hyperbolic geometry how many lines are there parallel to a given line through a given point?
infinitely many
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.
Which conjecture justifies the construction of a line parallel to a given line through a given point?
Euclid's parallel postulate.
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")
Why can rays be perpendicular but not parallel?
Rays pass through one point. Parallel lines never meet.
Can a given point be in two lines?
A point has an infinite amount of lines passing through it.
Do lines that aren't parallel always intersect?
Yes, they do. By definition, lines that never intersect must be parallel, so all non-parallel lines must intersect at some point. Given that they are normal lines (y=mx+b) they will always have a point that suffices the equation when they are set equal to each other.
How many lines can pass through A?
An infinite number of lines can pass through any given point.
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 a point on the horizon where parallel lines appear to meet?
A point on the horizon where parallel lines appear to meet is called the vanishing point.
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.
