Perpendicular Lines – Definition with Examples

What Is Perpendicular?

Two distinct lines intersecting each other at 90°, or a right angle, are called perpendicular lines. 

Example:

perpendicular lines

Here, AB is perpendicular to XY because AB and XY intersect each other at 90°.

Non-Example:

parallel linesintersecting line acute angleintersecting line right angle
The two lines are parallel and do not intersect each other. They can never be perpendicular to each other.The two lines are intersecting each other at an acute angle. So, they are not perpendicular.The lines are not intersecting each other at right angles.

Perpendicular Symbol

Perpendicular lines are represented by the symbol ‘’. Suppose, m and n are two lines intersecting each other at 90°, then they are perpendicular to each other and are represented as mn. The point of intersection of perpendicular lines is called the foot of the perpendicular.

Properties of Perpendicular Lines

  • 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. 
properties of perpendicular lines
  • Adjacent sides of a square and a rectangle are always perpendicular to each other.
Adjacent sides of a perpendicular
  • The sides of the right-angled triangle enclosing the right angle are perpendicular to each other.
Sides of right angle triangle


Real Life Examples

We can observe many perpendicular lines in real life. 

Some examples are the sides of a set square, the arms of a clock at certain times of the day, the corners of the blackboard, a window, and the Red Cross symbol. 

Perpendicular lines in real life


Difference between Perpendicular Lines and Parallel Lines

Perpendicular LinesParallel Lines
Perpendicular lines are lines that intersect at a 90° angle.Parallel lines are lines that are always the same distance apart. Parallel lines never intersect.
The symbol used to represent a perpendicular line is “⊥”.The symbol used to represent a parallel line is “||”.
Example: The corner of the postcardExample: Railway tracks
Perpendicular lines on corner of the postcard
Perpendicular lines on railway tracks
The corner of a rulerThe edges of a ruler
Perpendicular lines on corner of the ruler
Perpendicular lines on edge of the ruler


Construction of Perpendicular Lines

We can draw perpendicular lines for a given line in two ways.

  • Using a protractor
  • Using a compass

Drawing a perpendicular line using a protractor

Step 1: Let m be the given line and A the given point on it.

Step 2: Place the protractor on the line m such that its baseline coincides with m, and its center falls on A. 

Step 3: Mark a point B against the 90-degree mark on the protractor.

Step 4: Draw a line n passing through A and B.

Then line m ⊥ line n at A.

Draw perpendicular line using protractor

Drawing a perpendicular line at a given point on a line using a compass

Step 1: Place a compass tip on the given point A. Take an appropriate radius and draw an arc on either side of the given point.

Draw perpendicular line using compass

Step 2: Stretch the compass wider. Place the compass tip on the new points and make a small arc above the given line. The two new arcs will intersect.

tips for Draw perpendicular line using protractor

Step 3: Use the ruler to join the given point A and point B where the arcs intersect.

Arcs Intersect

Solved Examples on Perpendicular

Example 1: State whether a given set of lines are perpendicular or parallel.

Perpendicular Lines – Definition with Examples

(a)
(b)Perpendicular Lines – Definition with Examples
(c)Perpendicular Lines – Definition with Examples
(d)Perpendicular Lines – Definition with Examples

Solution:

  1. Parallel lines
  2. Perpendicular lines
  3. Perpendicular lines
  4. Parallel lines

Example 2: Write a relation between the line segments indicated by the arrow in each shape.

Parallel lines
(A)
Perpendicular lines
(B)
2 Perpendicular lines
(C)
Parallel lines
(D)

Solution: 

  1. AB ⊥ AE
  2.  PQ || SR
  3. PQ || NM
  4. AB ⊥ AD

Example 3: The diagonals of a rhombus are perpendicular to each other. How many right angles are formed at the intersection?

Diagonals of a Rhombus

Solution:

Since the lines AC and BD intersect each other at 90 degrees, there are 4 right angles at the intersecting point. 

∠AED = ∠DEC = ∠CEB = ∠BEA = 90 degrees

Example 4: Name some two-dimensional shapes that have perpendicular lines.

Solution:

Rectangle
Rectangle
Right Angled Triangle
Right-Angled Triangle
Square
Square

Practice Problems

Perpendicular

Attend this Quiz & Test your knowledge.

1

Identify the pair of perpendicular line segments in a given shape.

Perpendicular Lines – Definition with Examples
AG and AB
FE and ED
FE and CD
CB and AB
CorrectIncorrect
Correct answer is: FE and ED
FE and ED are perpendicular line segments.
2

Each object has a highlighted pair of lines. Which of this object highlighted pair of lines does not show perpendicular lines?

AA
BB
CC
DD
CorrectIncorrect
Correct answer is: A
Candle. Its highlighted pair of lines shows parallel lines.
3

At what time the hands of the clock will be perpendicular to each other?

12 o’clock
6 o’clock
3 o’clock
5 o’clock
CorrectIncorrect
Correct answer is: 3 o’clock
At 3 o’clock the hands of the clock are at 90 degrees to each other. So they are perpendicular to each other.
Perpendicular Lines – Definition with Examples
4

How many lines are perpendicular to line CD in a given figure?

Perpendicular Lines – Definition with Examples
1
2
3
4
CorrectIncorrect
Correct answer is: 3
Line PQ, line RS and line TU are perpendicular to CD. So, there are 3 lines perpendicular to line CD in the given figure.

Frequently Asked Questions

Perpendicular lines are those lines that intersect each other at 90 degrees.

These lines always intersect at right angles. 

The perpendicular symbol is ⊥. It is used between the two lines to show that they are perpendicular to each other.

Perpendicular lines intersect at right angles (90°) while parallel lines are parallel to each other and never intersect.

No, not all intersecting lines are perpendicular to each other. They may intersect at different angles other than 90 degrees.