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What defines two lines as parallel in space?
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Two lines are parallel in space if they are coplanar and do not intersect.
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How can you determine if a line is parallel to a plane?
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A line is parallel to a plane if it does not intersect the plane.
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What is the parallel postulate in geometry?
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The parallel postulate states that through a point not on a line, there is exactly one line parallel to the given line.
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How can you prove two planes are parallel?
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Two planes are parallel if they do not intersect, which can be shown if corresponding lines within the planes are parallel.
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What is the symbol for parallel lines?
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The symbol for parallel lines is '||'.
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Can a line be parallel to two planes at the same time?
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Yes, a line can be parallel to two planes if it is not intersecting either plane.
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What is a transversal line?
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A transversal line is a line that intersects two or more lines at distinct points.
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How do parallel lines behave in Euclidean geometry compared to non-Euclidean geometry?
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In Euclidean geometry, parallel lines never meet. In non-Euclidean geometry, the concept can differ, such as in hyperbolic geometry where lines may diverge.
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What is the relationship between skew lines and parallelism?
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Skew lines are non-coplanar lines that do not intersect and are not parallel.
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Can planes that intersect be parallel?
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No, planes that intersect cannot be parallel as they meet at a line.
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What is the relationship between parallel planes and lines?
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If two planes are parallel, then a line perpendicular to one plane is also perpendicular to the other plane.
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What is a real-world example of parallel planes?
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The floors of a two-story building represent parallel planes.
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What is the effect of parallelism on angles formed by a transversal line?
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If a transversal cuts parallel lines, it creates corresponding angles that are equal.
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How do you represent a plane parallel to a line in notation?
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You can represent a line 'l' parallel to plane 'P' as l || P.
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What geometric tool can you use to check for parallelism in 3D models?
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A protractor or parallel line indicator can be used along with visual inspection to check parallelism in models.
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