Parallel (geometry) facts for kids
Parallel is a term in geometry and in everyday life that refers to a property of lines or planes. Parallel lines or planes are next to each other, but never touch each other. This means they never intersect at any point. If two lines 
and 
are parallel, then we describe this by writing 
. The slopes of parallel lines are always equal.
Even if these two line segments were extended to infinity, there would never be a point of intersection between the two of them. In fact, two parallel lines in the two-dimensional plane are always a fixed distance apart.
Contents
Construction
Related pages
Images for kids
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Line art drawing of parallel lines and curves.
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The problem: Draw a line through a parallel to l.
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Intersecting, parallel and ultra parallel lines through a with respect to l in the hyperbolic plane. The parallel lines appear to intersect l just off the image. This is just an artifact of the visualisation. On a real hyperbolic plane the lines will get closer to each other and 'meet' in infinity.
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On the sphere there is no such thing as a parallel line. Line a is a great circle, the equivalent of a straight line in spherical geometry. Line c is equidistant to line a but is not a great circle. It is a parallel of latitude. Line b is another geodesic which intersects a in two antipodal points. They share two common perpendiculars (one shown in blue).
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Property 1: Line m has everywhere the same distance to line l.
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Property 2: Take a random line through a that intersects l in x. Move point x to infinity.
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Property 3: Both l and m share a transversal line through a that intersect them at 90°.
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See also
In Spanish: Paralelismo (matemática) para niños
