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What is meant by parallelism in geometry?
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Parallelism in geometry refers to the property of two or more lines, planes, or a line and a plane being the same distance apart over their entire length and never meeting.
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What does it mean for a line to be parallel to a plane?
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A line is parallel to a plane if they do not intersect and there is no point on the line that lies in the plane.
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How do you symbolically represent that a line is parallel to a plane?
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The symbol '||' is used to denote parallelism. For example, if line L is parallel to plane P, it is written as L || P.
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What is a condition for a line to be parallel to a plane?
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A line is parallel to a plane if it is parallel to a line that lies on the plane.
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What could indicate that a line is not parallel to a plane?
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If a line intersects the plane at any point, it is not parallel to the plane.
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Can a line be parallel to a plane and still intersect it?
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No, if a line intersects a plane at any point, it is not parallel to the plane.
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What is the relationship between a line parallel to a plane and the normal of the plane?
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A line parallel to a plane is perpendicular to the normal vector of the plane.
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Do parallel lines act the same way as parallel lines when it comes to planes?
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Yes, similar properties of parallelism apply to lines and planes as they do to parallel lines.
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If two planes are parallel and a line is parallel to one plane, is it parallel to the other plane?
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Yes, if two planes are parallel, a line parallel to one will be parallel to the other.
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How can you verify a line is parallel to a plane in 3D geometry?
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You can verify by ensuring the line's direction vector is perpendicular to the plane's normal vector.
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What is a real-world example of a line parallel to a plane?
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A railway track running parallel to the ground is an example.
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If a line lies above a plane and does not touch it, is it parallel?
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If it maintains a constant distance at all points, yes.
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If two parallel lines each sit on different planes, are the planes parallel?
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Not necessarily; the planes could still intersect elsewhere.
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In geometry, what term describes a line neither perpendicular nor parallel to a plane?
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Such a line is called an oblique line to the plane.
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What tool can help visualize the parallelism of a line and a plane?
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A 3D modeling software or geometric construction tools can help.
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