# Parallel lines

To speak of parallel lines we must understand that a **straight line** is a **succession** of forms **infinite** of **points** which are located all in a **same direction** , succession is characterized as so **continuous** and **indefinite** , is why we say that a straight it has neither beginning nor end. Then parallel lines are two lines that have no **point** in **common** , nor are **coincident**. Two lines that are located in a plane are parallel if they are either one and the same line or, on the contrary, if they are not sharing any point in common. Similarly, in **space they** can be **parallel** if they are one and the **same plane** or if they are not sharing **any point** .

## What are parallel lines?

Parallel lines are the lines that lie within a **same plane** and having the **same slope** and exhibiting no **point** in **common** , that is not **cross** or **touch** nor intersect in their **extensions** .

- Definition
- features
- Properties
- Distance between two parallel lines
- Objects with parallel lines
- Solved exercises
- Examples

## Definition

In order to explain and clarify the meaning of parallel lines, we must first give a brief explanation about the concept of what a **line is** ; and we can say then that a line is a **consecutive series** of **points** , which are all located in the same **direction** , and which have as characteristics being **continuous** and **infinite** , in other words, that they have no beginning or end.

Parallel lines are the type of **line** that maintains a certain **distance** from each other, and although they have the ability to extend their trajectory to infinity, they can never **meet** or touch at **any point** ; In other words, we understand by the name of parallel lines those lines that are located within the **same plane** , and that **do not** also have any **common point** between them and show the same slope, this means that they cannot **touch** or **cross** , not even its **extensions**they can cross between them, a clear example of the parallel lines that we see daily are the **train tracks.**

## features

The main **characteristics of parallel lines** are the following:

- Are always at the
**same distance**but**never**will**touch**each other . - Parallel lines or lines are always pointing in the
**same direction**. - When the parallel lines intersect with another line, which is known as
**Transversal**, it can be seen that the**angles**are equal. - Parallel lines have a pair of
**corresponding**and**equal****angles**. - They have a pair of alternate
**interior angles**of equal measure.

## Properties

Among the properties that we can mention with respect to a parallel line are:

- It has
**symmetry**, which means that one line is parallel to another, for this reason, it will be**parallel**to the**first**. - They are
**reflective**because every line is parallel to itself. - Parallel lines have a
**corollary**, all parallel lines have the same direction; corollary of the transitive p, two parallel lines with respect to a third will be**parallel to**each other; and**transitive**, if a line is parallel to another and at the same time to a third, then the first will be parallel to the third line. - They have a
**perpendicularity**relationship which occurs between two lines, where at a certain point the lines are divided resulting in four**right angles**, in other words four angles with a measure of**90 °**each; We can see this, for example, at the intersection of two streets where you can clearly see the four right angles that are formed at each corner.

## Distance between two parallel lines

The distance that exists between two lines that are parallel is the same as the **distance** that exists from **any point** on one of the **lines** to the other **line** .

## Objects with parallel lines

Some of the objects in which we can find parallel lines are:

- On a wall, at the junction of its corners.
- In a window with double division (in the shape of a cross).
- In the corner of a door.
- It could be the junction of a utility pole with the floor.
- The diagonal of a pizza box.
- The train lines.
- At a street intersection.

## Solved exercises

Some examples of exercises already solved with respect to parallel lines are the following:

**Determine the value of t so that the following lines are parallel:**

**r: 3x – 4y + 12 = 0**

**s: tx + 8y – 15 = 0**