# Category:Parallel

This category contains results about **Parallel** in the context of **Geometry**.

Definitions specific to this category can be found in Definitions/Parallel.

### Lines

In the words of Euclid:

**Parallel**straight lines are straight lines which, being in the same plane and being produced indefinitely in either direction, do not meet one another in either direction.

(*The Elements*: Book $\text{I}$: Definition $23$)

The contemporary interpretation of the concept of parallelism declares that a straight line is parallel to itself.

### Planes

Two planes are **parallel** if and only if, when produced indefinitely, do not intersect at any point.

In the words of Euclid:

**Parallel planes**are those which do not meet.

(*The Elements*: Book $\text{XI}$: Definition $8$)

The contemporary interpretation of the concept of parallelism declares that a plane is parallel to itself.

### Line Parallel to Plane

Let $L$ be a straight line.

Let $P$ be a plane.

Then $L$ and $P$ are **parallel** if and only if, when produced indefinitely, they do not intersect at any point.

## Subcategories

This category has the following 3 subcategories, out of 3 total.

### P

- Parallel Planes (empty)