paralelas

Paralelas, or parallels, are lines in the same plane that do not meet regardless of how far they are extended. In Euclidean geometry, a key property is that through a given point not on a line there exists exactly one line parallel to the original line. This makes parallelism an equivalence relation among lines: parallel lines are lines that share the same direction and never intersect.

Two non-vertical lines are parallel if they have equal slopes; vertical lines are parallel if they share the same x-coordinate, in effect having undefined but identical directional orientation. The distance between two parallel lines remains constant along their length, measured along a line perpendicular to both.

The concept extends to three dimensions with parallel planes: two planes are parallel if they do not intersect. In geometry, parallelism thus describes a uniform directional relationship in space.

Non-Euclidean geometries offer different viewpoints on parallels. In hyperbolic geometry, through a given point not on a line there are infinitely many distinct parallels. In elliptic geometry, no parallel lines exist because all lines eventually intersect.

Geographically, the term parallels is commonly used for lines of constant latitude on Earth. These parallels are circles lying in planes parallel to the equatorial plane and are equidistant from each other when projected onto the globe, with notable examples including the equator and the Tropics.

Etymology: the word derives from Latin parallelus, from Greek parallelos, meaning “beside one another.”