Parallelism is Reflexive Relation

Theorem
Let $S$ be the set of straight lines in the plane.

For $l_1, l_2 \in S$, let $l_1 \parallel l_2$ denote that $l_1$ is parallel to $l_2$.

Then $\parallel$ is a reflexive relation on $S$.

Proof
By definition of parallel lines, the contemporary definition is for a straight line to be declared parallel to itself.

Hence for a straight line $l$:
 * $l \parallel l$

Thus $\parallel$ is seen to be reflexive.

Also see

 * Parallelism is Symmetric Relation
 * Parallelism is Transitive Relation


 * Parallelism is Equivalence Relation