zero
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.
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.
A point has an infinite amount of lines passing through it.
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.
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.
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.
infinitely many
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.
Euclid's parallel postulate.
The Playfair Axiom (or "Parallel Postulate")
Rays pass through one point. Parallel lines never meet.
A point has an infinite amount of lines passing through it.
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.
An infinite number of lines can pass through any given point.
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.
A point on the horizon where parallel lines appear to meet is called the vanishing point.
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.