Difference Between Parallel and Perpendicular

By: | Updated: Dec-31, 2022
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It just took a moment to understand that lines are all over the place. When we move, act and speak, we create lines everywhere. It’s amazing to think how lines are all over the place. They appear anywhere you look. But we are so busy and so immersed in our own thoughts that we do not even notice that lines exist.

Summary Table

Parallel Perpendicular
Lines that never cross each other and have a constant separation between them are said to be parallel. Lines that always cross one another at a right angle are said to be perpendicular.
Parallel lines are represented by the symbol ||. Using the ⊥ symbol, perpendicular lines are identified.
Parallels are described by the equation y = mx + b. Y = mx + an is the perpendicular equation.

 

Railroad tracks and the totally different perspective of a whiteboard are examples of parallel lines. A room’s adjoining walls and the letter L are two examples of perpendicular lines.

Difference Between Parallel and Perpendicular

Lines are constantly being drawn. They are straight and they never get in the way of anything. When we draw lines, we are demonstrating that we are really interested in what is going on everywhere. Lines are like a steady line that can be drawn in any direction that we want it to go. They are like a perfectly round circle with an infinite diameter.

Lines are like a straight path which is endless. They span endlessly in both directions. Lines are perfect; their length is endless. Lines are very flexible, they can extend infinitely. We make lines that are either very long or very short. We make curves and wiggles in our lines. Some lines are very long, some are very narrow, and some are quite fine.

This article describes the difference between parallel and perpendicular lines. Continue to read to learn more about these terms.

What is Parallel?

Lines that do not cross or join at any point in a plane are called parallels, because they do not cross or join at any point in a plane. They will never meet each other at any point and are not even. Parallel, or paralleled lines, are those that are straight and do not intersect. Parallel lines do not intersect but instead cross paths at all points in the same plane.

Two planes are called parallel if their lines do not intersect at any point and continue to run straight along one another. Lines that do have a special intersection point and which always meet at an equal distance are called parallel lines. Parallel lines can be visualized by using the graphic that looks like a ‘||’.

You probably already have examples like a table, a chair, a staircase, a drawer, a door, etc. You certainly see a lot of lines like this. It is very common to see multiple lines that go across each other but we are not really aware of them.

Two lines do not intersect because there are no planes that can cross or overlap each other. They are very far from each other. Two planes have the same slope and have the same length; they have the same height and they will not meet. Note that, for lines to be parallel, they should lie on the exact plane in which they are placed.

Difference Between Parallel and Perpendicular

What is Perpendicular?

Lines do not always cross. When two lines are oriented at a right angle, those two lines are called perpendicular. When lines cross at an angle that is 90°, that is, when the angle is 90°, the lines that meet are said to be perpendicular.

Perpendicularly, a line is parallel to another line but at a certain angle. When two straight lines intersect at 90°, the angle between them is called perpendicularity. Those lines that intersect with each other at right angles form a right angle.

Perpendicular means that a line is perpendicular to the plane that it crosses or perpendicular to the point where it intersects another line. At the intersection of two lines, they form 4 angles that are exactly the same and all are at exactly the same level.

If lines are perpendicular to points in the same line or are perpendicular to lines in any plane in which they intersect, then the lines on which they are perpendicular to every point on which they intersect. Two plane surfaces are considered to have an angle of perpendicular if their intersection with another plane is a straight line.

How are They Related?

Geometry’s use of parallel and perpendicular lines is crucial, and their distinctive characteristics make it simple to distinguish between them. If two lines are in the same plane, are spaced equally apart, and never cross one another, they are said to be parallel. Perpendicular lines are those that cross at an angle of 90 degrees.

Two straight lines are said to be parallel if they are located in the same plane and never cross one another. They are equidistant lines that are always spaced equally apart. On the other hand, two lines are said to be perpendicular when they cross each other at a 90° angle.

Two equally spaced lines that will never cross or touch each other at any point are said to be parallel. The lines have the same slope and a zero angle because they are equally spaced apart. On the other hand, two lines are said to be perpendicular when they cross at a right angle. At the points where the two intersecting lines meet, there are four equal, 90-degree angles that are formed. Two perpendicular lines’ slopes are opposite reciprocals of one another.

What are the Differences?

The function

If two non-vertical paths are equally spaced along their entire length and have the same slope, they are said to be parallel. In geometry, parallel lines are referred to as those that never intersect and are equally spaced apart in every direction. Not all lines can be parallel. The lines are considered to be perpendicular to one another when two connected lines form four equal and right-angle angles at their points of intersection. When two lines intersect at a right angle, they are perpendicular.

The Slope

When two lines are equally spaced apart from one another and never cross or touch, they are said to be parallel. The lines have the same slope, which means that their distance from one another is the same throughout because they are equally spaced apart. The slope of two parallel lines is equal, to put it simply. On the other hand, the slope of perpendicular lines is the negative reciprocal of itself, which means that the lines cross one another at a right angle.

The Symbol

Two straight lines serve as the parallel line symbol. A right angle intersection of two lines is used to symbolize a perpendicular line.

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