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Do Through a point not on a line one and only one line always can be drawn parallel to the given line?
True
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.
Point A lies outside of plane P How many planes can be drawn through point A?
Infinite planes can be drawn through point A that lies outside plane P. Each plane can be oriented differently, intersecting plane P at various angles, or not intersecting it at all. The only constraint is that the planes must pass through point A, allowing for countless possibilities in their orientation.
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.
Is the tangent of a circle is parallel to the radius drawn to the point of tangency?
Yes it is. Great work!
Do Through a point not on a line one and only one line always can be drawn parallel to the given line?
True
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 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.
Is the tangent of a circle is parallel to the radius drawn to the point of tangency?
Yes it is. Great work!
How many tangents can be drawn from a single point?
Two tangents can be drawn from a point outside a circle to the circle. The answer for other curves depends on the curve.
How many tangents can be drawn to a circle containing a point outside the circle?
Any tangent must contain a point outside the circle. So the answer to the question, as stated, is infinitely many. However, if the question was how many tangents to a circle can be drawn from a point outside the circle, the answer is two.
What is the name of the shape formed when two lines are drawn away from a single point?
That is called an angle.
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.
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."
How many line can be drawn through two point in a plane?
One.
How many rays can be drawn through one point?
Infinitely many.
