Perpendicular Lines – Definition with Examples

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Definition of Perpendicular Lines

In geometry, perpendicular lines are defined as two lines that meet or intersect each other at right angles (90°). The term ‘perpendicular’ originated from the Latin word ‘perpendicularis,’ meaning a plumb line. 

If two lines, AB and CD, are perpendicular, then we can write them as AB ⟂ CD. The symbol ⟂ is used to indicate that the lines are perpendicular.

Perpendicular Lines – Definition with Examples


Examples of Perpendicular Lines in Real Life

We can observe many perpendicular lines in real life. Some examples are shown below.

Perpendicular Lines in Real Life - SplashLearn


Non-Examples of Perpendicular Lines in Real Life

Non Example of Perpendicular Lines in Real Life - SplashLearn
The two lines are parallel and do not intersect each other. The two lines are intersecting each other at an acute angle. The lines are not intersecting at right angles.

Properties of Perpendicular Lines

The two main properties of perpendicular lines are given below.

  1. These lines always intersect at right angles.
  2. If two lines are perpendicular to the same line, they are parallel to each other and will never intersect. 
Properties of Perpendicular Lines - SplashLearn


Constructing Perpendicular Lines 

We can draw perpendicular lines in the following ways. 

Using a Protractor

  • Draw a horizontal line, PQ, on a sheet of paper. 
  • Mark a point, A, on it. This would be the point of intersection.
  • Place the center of the protractor on Point A. Align the baseline of the protractor with the line PQ. 
  • At the 90° mark on the protractor, mark Point B. It is at the very top of the protractor. 
  • Join points A and B to get AB ⟂ PQ.
Draw Perpendicular Lines using Protractor - SplashLearn


Using a Compass

  • Draw a line, PQ, using a ruler. Mark a point A on it.
  • Draw an arc of any radius on either side of Point A. The arc length should be the same on both sides. 
  • Mark the points where the arcs intersect the line as X and Y.
  • Place the compass needle at point X and set a radius greater than XA. Draw an arc from X in the upper part of the line PQ. 
  • Keep the radius the same and cut an arc from Point Y, intersecting the previous arc at B. 
  • Join A and B using a ruler. Extend it if needed. The lines AB and PQ are perpendicular to each other. 
Draw Perpendicular Lines using Compass - SplashLearn
Draw Perpendicular Lines using Compass 2 - SplashLearn
Draw Perpendicular Lines using Compass 3 - SplashLearn


Conclusion
Give your children opportunities to observe perpendicular lines in objects or places around them, such as a tall tree on the ground, an electric pole on the pavement, railway intersection, the corner of two adjacent walls, and high buildings.

If you wish to explore the meaning, history, or tips to excel in any topic, SplashLearn presents an entertaining platform for you. Read the informational blog posts to gain knowledge and practice with fun and entertaining educational games. Start learning today!

Solved Examples

Example 1 If AB ⊥ CD and CD ⊥ EF. What can you say about AB and EF? 

Line AB is perpendicular to line CD. 

Also, line CD is perpendicular to line EF. 

When two lines are perpendicular to the same line, then the two lines are parallel to each other. 

Thus, lines AB and EF are parallel to each other. 

Example 2: Are these lines perpendicular?

Solved Example of Perpendicular Lines

No, these lines are not perpendicular because they do not intersect at right angles.

Example 3: Are these lines perpendicular?

Solved Example of Perpendicular Lines 2

Yes, these are perpendicular lines. They intersect at 90°.

Practice Problems

Perpendicular Lines

Attend this Quiz & Test your knowledge.

1At what time will the hands of the clock be perpendicular?

03:40 pm
04:00 pm
09:00 am
10:10 am
CorrectIncorrect
Correct answer is: 09:00 am
The hands of the clock intersect at right angles when the time is 9:00 am.
Perpendicular Lines – Definition with Examples

2Perpendicular lines intersect each other at _____ angle.

right
obtuse
acute
straight
CorrectIncorrect
Correct answer is: right
Perpendicular lines intersect each other at 90°. 90° angles are known as right angles.

3In which of the following objects can we find perpendicular lines?

Ball
Birthday Hat
Banana
Laptop
CorrectIncorrect
Correct answer is: Laptop
Laptop has edges intersecting at right angles. All other images do not have lines intersecting at right angles.

Frequently Asked Questions

We can define a perpendicular line as two straight lines joined at a common point, making a 90° angle with each other.

Graphically, parallel lines are two or more straight lines that do not touch each other even after extending them. However, perpendicular lines intersect each other at 90°.

No. All intersecting lines are not perpendicular lines as a perpendicular line is made by two lines intersecting at 90°.

Parallel lines never touch each other while perpendicular lines meet each other at the intersecting point. Thus, you cannot have two lines that are both parallel and perpendicular to each other. 

A perpendicular line must be at 90° with the other line. Since you can draw many lines in this manner, there can be an infinite number of perpendicular lines on a given line. 


Perpendicular Lines – Definition with Examples

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Perpendicular Lines – Definition with Examples

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Perpendicular Lines – Definition with Examples

Parallel and Perpendicular Lines

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