Parallel (geometry) facts for kids
In geometry, the word parallel describes lines or flat surfaces (called planes) that are always the same distance apart. Imagine two straight roads that run side-by-side forever without ever meeting. That's what parallel means!
Parallel lines or planes never touch each other, no matter how far they are extended. This means they will never cross at any point. If you have two lines, let's call them line 1 and line 2, and they are parallel, we can write it like this: line 1 || line 2.
A cool thing about parallel lines is that their slopes are always exactly the same. If one line goes up by 2 units for every 1 unit it goes across, a parallel line will do the exact same thing. Even if these lines went on forever, they would always stay the same distance apart.
How to Draw Parallel Lines
Drawing a line that is parallel to another line is a fun challenge in geometry. You can do it using a compass and a straightedge (like a ruler, but you only use it for drawing straight lines, not measuring). The basic idea is to create angles that are equal, which forces the lines to be parallel.
One common way to construct a parallel line is by using a transversal line (a line that crosses two other lines) and making sure the angles it creates are the same. For example, if you draw a line and then another line that crosses it, you can use your compass to copy one of the angles to a new spot. When you draw a line through that new angle, it will be parallel to your first line.
What Else is Parallel?
Parallel ideas pop up in many areas of geometry. Here are a few related terms:
- Parallelogram: This is a special type of four-sided shape where opposite sides are parallel and equal in length. Think of a squashed rectangle!
- Parallel postulate: This is a famous rule in geometry that helps us understand how parallel lines work. It basically says that through any point not on a given line, there is only one line parallel to the given line.
- Perpendicular: This is the opposite of parallel. Perpendicular lines meet or cross each other at a perfect 90-degree angle, like the corner of a square.
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
