Parallel lines

Parallel lines are coplanar straight lines that never intersect. In Euclidean geometry, they remain a constant distance apart.

Euclidean geometry: The geometry of points, lines, and shapes governed by Euclid’s postulates. Its parallel postulate makes the familiar constant-distance definition possible.
Transversal (geometry): A line that intersects two or more other lines at distinct points. Its intersections expose angle patterns that reveal whether lines are parallel.
Hyperbolic geometry: A non-Euclidean geometry in which infinitely many lines through a point do not meet a given line. It replaces Euclid’s unique parallel with many nonintersecting choices.
Parallel projection: A projection in which all projectors are parallel to one another. It preserves parallel directions when representing three-dimensional objects.
Line (geometry): A straight, one-dimensional geometric object extending infinitely in both directions. Parallelism compares entire lines, not merely finite segments.
Corresponding angles: Angles occupying matching positions where a transversal crosses two lines. Equal corresponding angles are a standard test for parallel lines.
Elliptic geometry: A non-Euclidean geometry in which any two lines intersect. It has no parallel lines, unlike the Euclidean plane.
Perspective (graphical): A drawing method that represents depth through lines converging toward vanishing points. Its apparent convergence contrasts with parallel projection’s unchanged directions.
Plane (geometry): A flat, two-dimensional surface extending infinitely in every direction. The definition requires both lines to lie in the same plane.
Alternate interior angles: A pair of angles between two lines and on opposite sides of a transversal. Their equality follows from parallelism and can also establish it.

Linked from 17 pages