Geometry has introduced us to a number of various terms, theories, formulas, definitions, and diagrams. The two most common and widely used terms or definitions in the subject of geometry are parallel and perpendicular.

Both the terms or definitions are very different and unique from each other and don’t share any common similarities.

**Parallel vs Perpendicular**

The difference between parallel and perpendicular is that the former don’t intersect each other and run parallel to each other while on the other hand, the latter intersect each other at a right angle (it is measured as 90°). Both the terms are quite common in geometry and have their own symbols and equations.

Parallel lines or curves or 3 D structures don’t meet each other at any point. They could refer to either parallel lines on a notepad, opposite sides of a ladder, opposite sides of a road, or opposite sides of a railway track.

These could refer to either lines, boxes, diagrams, or curves.

Perpendicular lines or 3-dimensional figures or curves intersect each other at a particular point. These often form right angles with each other.

They refer to either the steps and sides of a ladder, railway track crossing, designs in the window, etc. They have and are represented by a unique symbol and equation.

**Comparison Table **

Parameters Of Comparison | Parallel | Perpendicular |
---|---|---|

Significance | Parallels lie at a certain distance from each other and do not intersect. | Perpendiculars lie close to each other and are at a right angle to each other. |

Equation | The equation for parallels is y = mx + b. | The equation of perpendiculars is y = mx + a. |

Symbol | The symbol in this case is represented by two straight lines. | The symbol in this case is represented by two lines intersecting each other at a right angle. |

Intersection | Parallel lines or curves always maintain a distance and hence never intersect each other. | Perpendicular lines or curves intersect each other at a right angle. |

Examples | A few examples of Parallels are: •Lines of pages •Telecom Wires | A few examples of Perpendiculars are: •Football Field •Railway Tracks |

**What is Parallel?**

A Parallel could either refer to figures, curves, lines, or 3-dimensional boxes. It signifies two lines or curves that run parallel and never intersect.

They are quite similar to the symbol of an equal sign.

The subject of English defines parallel as an event or happening that occurs at the same time. It refers to events being connected or moving forth in a forward direction.

The English and mathematical terms are quite different from each other.

Parallel lines are represented by two parallel line bars that run parallel to each other. Their symbol is designed as two straight lines at an angle of zero degrees.

The equation y = mx + b represents this term. The “m” remains the same for both the parallel lines.

Parallels often obey a property called transitive property. According to this property if line A is parallel to line B and line B is parallel to line C then both lines A and C are parallel to each other.

This is one of the most famous and well-known properties of parallel figures

There are a number of examples that represent or help us understand parallel lines. These examples are listed below:

- The opposite sides of a figure are like a rectangle.
- Zebra crossings.
- Staircase.
- Railings.
- The edges of a sidewalk or a roadway.

**What is Perpendicular?**

Perpendiculars could either refer to lines, curves, boxes, or 3-dimensional figures. They run perpendicularly and intersect at a particular point.

The point of intersection is a right angle in the case of perpendicular figures.

Perpendicularity is often described or exhibited in terms of a particular symbol. They also have an equation of their own.

It follows the transitive property according to which if line X is perpendicular to line Y which is perpendicular to line Z then line X becomes perpendicular to line Z.

Right angles or ninety-degree angles often depict perpendicular rays. They are calculated, measured, and constructed with the help of a Pythagoras theorem.

This theorem and method are used in laying a number of fields, gardens, and other large areas.

A number of examples help us understand perpendicular rays and give us a brief idea of the term. Some of these examples are:

- Designs of a window.
- Football field.
- The crossings of a railway track.
- A house with a wall that lies perpendicular to the floor and ceiling.
- The “plus” sign of a first aid kit or box.

The lines in this case are exactly vertical and straight. The letter “T” consists of two lines that lie perpendicular to each other. They lie at a right angle to each other.

**Main Differences Between Parallel and Perpendicular**

- Parallel figures run at some distance from each other whereas perpendicular figures run quite close to each other meeting at a point.
- The Intersection doesn’t take place in the case of parallel while on the other hand, the intersection is a common occurrence in the case of perpendiculars.
- Parallel figures don’t include a 90° angle while on the other hand, perpendicular figures have got a right angle.
- Lines of a roadway refer to parallel dimensions whereas perpendicular window frames represent perpendiculars.
- The slopes of parallel diagrams are equal to each other while on the other hand, the slopes of perpendicular diagrams are unequal to each other.

**References**

- https://books.google.com/books/about/Euclid_s_Window.html?id=GHY6VM3NsIwC#v=onepage&q&f=false
- https://pubs.nctm.org/view/journals/mtms/9/2/article-p84.xml

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