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.
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Examples of Perpendicular Lines in Real Life
We can observe many perpendicular lines in real life. Some examples are shown below.
Non-Examples of Perpendicular Lines in Real Life
| 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.
- These lines always intersect at right angles.
- If two lines are perpendicular to the same line, they are parallel to each other and will never intersect.
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.
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.
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.
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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?
No, these lines are not perpendicular because they do not intersect at right angles.
Example 3: Are these lines perpendicular?
Yes, these are perpendicular lines. They intersect at 90°.
Practice Problems
Perpendicular Lines
At what time will the hands of the clock be perpendicular?
The hands of the clock intersect at right angles when the time is 9:00 am.
Perpendicular lines intersect each other at _____ angle.
Perpendicular lines intersect each other at 90°. 90° angles are known as right angles.
In which of the following objects can we find perpendicular lines?
Laptop has edges intersecting at right angles. All other images do not have lines intersecting at right angles.
Frequently Asked Questions
What are perpendicular lines?
We can define a perpendicular line as two straight lines joined at a common point, making a 90° angle with each other.
What is the difference between parallel and perpendicular lines?
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°.
Are all intersecting lines also perpendicular lines?
No. All intersecting lines are not perpendicular lines as a perpendicular line is made by two lines intersecting at 90°.
Is it possible to have two lines that are both parallel and perpendicular to each other?
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.
How many perpendicular lines can be drawn to a given line?
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.