Perpendicular Lines

In perpendicular lines when two intersecting lines a and b are said to be perpendicular to each other if one of the angles formed by them is a right angle.

In other words,

If two lines meet or intersect at a point to form a right angle, they are called perpendicular lines. We can draw a perpendicular line with the help of a set of square.

The symbol used for perpendicular lines are .

For example, a b (read as a is perpendicular to b).

Perpendicular Lines Ab and AC

In the above figure, AB and AC are perpendicular lines. ∠CAB = 90°. We use the symbol ⊥ to represent perpendicular lines.


What are perpendicular lines in geometry?

Lines that meet or cross at right angle are perpendicular to one another.

Perpendicular Lines

A right angle is usually marked by a box as shown in the above figure. Two rays or two line segments are said to be perpendicular if the corresponding lines determined by them are perpendicular. Similarly a ray and a segment are said to be perpendicular if the corresponding lines determined by them are perpendicular.

Here, l m (read as l is perpendicular to m).


Look at the following pictures and observe that how stumps of a wicket are placed on the ground. If we represent the ground by a straight horizontal line and a stump with a vertical line, the set of such lines are called perpendicular lines.

Perpendicular Lines Examples

Look at the two lines PQ and RS which intersect at the point P. 

Intersect at the Point P

These lines are perpendicular to each other.


Look at the picture of the room:

Wall Perpendicular to Floor

Wall is perpendicular to the floor.

The lines in the corner along the wall and the floor (marked by red colour in the above figure) are perpendicular to each other.


Look at the road AB and CD. 

Perpendicular Roads

These roads are perpendicular to each other. The lines marked by red colour in the figure are perpendicular to each other.




Look at the two lines AB and CD which intersect each other at the point O. These two lines are perpendicular to each other.

Perpendicular Lines




We use the symbol  for perpendicular. In the figure, line segments AB and CD are perpendicular to each other. We write it as AB ⊥ CD or CD ⊥ AB.

Symbol for Perpendicular


(i) To draw a line perpendicular to a given line at a point on it with a set square:

Let AB be a line and C a point on it.

We want to draw a line perpendicular to AB at C with a set square.

Perpendicular Lines Drawing

Place a ruler along the line AB. Then place a set square so that its one of the perpendicular edges may fall along the ruler and the vertex at which they are perpendicular falls on C. Draw a line CD along the edge of the set square perpendicular to AB. Now remove the set square and the ruler.

CD is the required line perpendicular to AB at C.


(ii) To draw a line perpendicular to a given line from a point not on the line with a set square:

Let AB be a line and C a point not on the line.

We want to draw a line perpendicular to AB and passing through C.

Perpendicular Lines AB and CD

Place a ruler along the line AB. Then place a set square so that its one of the perpendicular edges may fall along the ruler and the edge of the set square perpendicular to the ruler passes through C. Draw a line CD along the edge of the set square which is perpendicular to the line AB.

Now remove the set square and the ruler.

CD is the required line perpendicular to AB passing through C.

You might like these

Quadrilaterals.

Elements of a Quadrilateral.

Types of Quadrilaterals.

Parallel Lines.

Perpendicular Lines.

Construction of Perpendicular Lines by using a Protractor.

Sum of Angles of a Quadrilateral.

Worksheet on Quadrilateral.

Practice Test on Quadrilaterals.





5th Grade Geometry Page

5th Grade Math Problems

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