Given a straight line L and a point A outside the straight line, find a straight line passing through point A and parallel to L, draw an arc R with a radius greater than the distance from A to L with point A as the center, intersect with the straight line L at point B, draw an arc with the same radius with point B as the center, and intersect with the straight line L in the same direction at point C. Draw an arc with the same radius with C as the center, intersect with the arc R at point D, and connect A and D (non-point B), then the straight line AD is the straight line.

It is proved that AB = DC and AD = BC, so the quadrilateral ABCD is a parallelogram, so AD//BC.

In geometry, two straight lines that never intersect (and never overlap) on the same plane are called parallel lines.

Parallel lines are important concepts in axiomatic geometry. The parallel axiom of Euclidean geometry can be expressed as "only one straight line is parallel to the known straight line at a point outside the straight line". However, its negative form "there is no straight line parallel to the known straight line at a point outside the straight line" or "there are at least two straight lines parallel to the known straight line at a point outside the straight line" can be used as a substitute for the parallel axiom of Euclidean geometry, and non-Euclidean geometry independent of Euclidean geometry can be deduced.

If both lines are parallel to the third line, then the two lines are also parallel to each other. If a∨b, b∨c, then a ∨ c.

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Baidu encyclopedia-parallel lines