# Category:Parallel Lines

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This category contains results about **Parallel Lines**.

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.

## Subcategories

This category has the following 2 subcategories, out of 2 total.

### P

## Pages in category "Parallel Lines"

The following 23 pages are in this category, out of 23 total.

### E

### P

- Parallel Chords Cut Equal Chords in a Circle
- Parallel Lines remain Parallel under Affine Transformation
- Parallel Lines which intercept Equal Segments on Transversals
- Parallelism implies Equal Alternate Angles
- Parallelism implies Equal Alternate Angles, Corresponding Angles, and Supplementary Interior Angles
- Parallelism implies Equal Corresponding Angles
- Parallelism implies Supplementary Interior Angles
- Parallelism is Equivalence Relation
- Parallelism is Equivalence Relation/Transitivity
- Parallelism is Reflexive Relation
- Parallelism is Symmetric Relation
- Parallelism is Transitive Relation
- Point at Infinity of Intersection of Parallel Lines