**Table of Contents**

1. | Introduction |

2. | Parallel Lines |

3. | Skew Lines |

4. | Perpendicular lines |

5. | Parallel Lines in real life |

6. | Perpendicular lines in real life |

7. | Equivalence Relation |

8. | Summary |

9. | FAQs |

29 October 2020

**Read time: 5 minutes**

**Introduction**

'Parallel and perpendicular lines', you might think these are just types of lines and how will it impact real life, but after going through this blog, I assure you that your perception regarding these lines will change.

**Parallel lines**

Parallel lines are nothing but lines in a plane that do not meet.

We can also say parallel lines are straight lines in a plane that do not intersect at any common point.

In simple for easy understanding, I would say, “Lines in a plane that do not meet each other, simultaneously have no common point” are said to be parallel.

**Skew Lines**

These lines exist in two dimensions and three dimensions of geometry. In three-dimensional geometry, we come across a new line that is ‘skew lines’. These lines are nothing but two lines but do not intersect and they are also not parallel.

The main difference between parallel and skew lines is that the former lies in the same plane but the latter lies in the different planes.

**Interesting facts about parallel lines**

We can call interesting facts mathematically as properties.

Let us see a few of them.

- Parallel lines are always equidistant from each other.
- They do not meet at any common point.
- They can be extended indefinitely in both directions.
- Parallel lines are coplanar lines.
- If m
_{1}and m_{2}are the slopes of two lines, if they are parallel, we say

\[m_1 = m_2\]

**Perpendicular Lines**

Two distinct lines intersecting each other at a right angle are called perpendicular lines. These lines touch each other at one point.

In smaller classes, we have gone through elementary geometry where perpendicular lines mean the relationship between two lines which meet at a point and the point to a right angle other.

Interesting facts about perpendicular lines

- This line always intersects at right angles.
- If two lines are perpendicular to the same line, they are parallel and will never intersect.
- Perpendicular lines always intersect, but the converse is not true; that is we can't say intersecting lines are always perpendicular.
- If two lines are perpendicularly representing the slope then

\[m_1 \times m_2 = -1.\]

**Parallel lines in real life**

First, we see a practical example. Let us take two cities

Delhi and Bhopal. There is a zero percent possibility that these two cities meet each other.

They don’t have a common point to meet.

In real life, we see parallel lines in:

- Railway tracks
- Four-way lanes, six-way lanes of roads
- Opposite sides of blackboard and whiteboard
- Opposite walls or doors in a room
- Arrangement in a queue

*Railway track with parallel lines*

**Perpendicular lines in real life**

In real life, the following are examples of perpendicular lines:

- Football field
- Railway track crossing
- First aid kit
- Construction of a house in which floor and the wall are perpendiculars
- Television
- Designs in windows

*Television with perpendicular edges*

**Equivalence Relation**

There is a relation called equivalence relation which relates parallelism and perpendicularity, which is defined by reflexive, symmetric, and transitive.

Take three friends A, B, and C

**Reflexive**

Any friend is a friend to himself, which is known as reflexive, which is a simple fact that always I love myself; this is fundamental psychology.

**Symmetric**

Let us take two friends A and B if A is a friend of B, then B is a friend of A which is denoted by perpendicularity that is A perpendicular to B and B perpendicular to A. They are meeting each other on a common point.

**Transitive**

Take three friends A, B and C. Three are a friend to each other which we can relate to parallel lines that is A is a friend to B, B is friend to A and B friend to C and C to A which can be well represented by three parallel lines standing one after another not intersecting or meeting each other but in practical life meeting through online mode via Skype, Zoom according to the latest technology.

If three conditions are satisfied, it is known as equivalence relations.

**Summary**

Parallel and perpendicular lines are making its application in a vast area. Though we learned a few, it is up to the reader to explore more things on these lines, which would be more interesting for them to go ahead. These lines help many people in fulfilling their activities in daily life.

**Frequently Asked Questions (FAQs)**

## Do parallel lines meet?

No parallel lines do not meet or intersect each other.

## What are perpendicular lines?

Two lines intersecting each other at a right angle are called perpendicular lines.

## What angles do perpendicular lines intersect at?

Perpendicular lines intersect at 90°.

## What are some examples of parallel lines in real life?

In real life railway track roads, the markings on the streets, the edges of sidewalks, a box of color pencils neatly arranged one by one is a few examples of parallel lines.

## What are some examples of perpendicular lines in real life?

Railway crossing, first aid kit symbol, football field, television set, etc