The parallel symbol is $${\displaystyle \parallel }$$. For example, $${\displaystyle AB\parallel CD}$$ indicates that line AB is parallel to line CD. See more

In non-Euclidean geometry, the concept of a straight line is replaced by the more general concept of a geodesic, a curve which is locally straight with respect to the metric (definition … See more

• Clifford parallel
• Collinearity
• Concurrent lines
• Limiting parallel
• Parallel curve
• Ultraparallel theorem See more

Two lines in a plane
Conditions for parallelism
Given parallel straight lines l and m in Euclidean space, … See more

If l, m, n are three distinct lines, then $${\displaystyle l\parallel m\ \land \ m\parallel n\ \implies \ l\parallel n.}$$
In this case, parallelism is a transitive relation. However, in case l = n, the superimposed lines are not considered parallel in … See more

• Papadopoulos, Athanase; Théret, Guillaume (2014), La théorie des parallèles de Johann Heinrich Lambert : Présentation, … See more