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Parallelism in geometry refers to the relationship between two lines or planes that never meet, no matter how far they are extended. This concept is important because it helps us understand and describe shapes, build structures, and solve mathematical problems involving distances and angles.
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Line art drawing of parallel lines and curves.
In geometry, parallel lines are coplanar infinite straight lines that do not intersect at any point. Parallel planes are infinite flat planes in the same three-dimensional space that never meet. In three-dimensional Euclidean space, a line and a plane that do not share a point are also said to be parallel. However, two noncoplanar lines are called skew lines. Line segments and Euclidean vectors are parallel if they have the same direction or opposite direction (not necessarily the same length).