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

From Perpendicular Lines to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Volume of a Cuboid | Volume of Cuboid Formula | How to Find the Volume

    Jul 20, 25 12:58 PM

    Volume of Cuboid
    Cuboid is a solid box whose every surface is a rectangle of same area or different areas. A cuboid will have a length, breadth and height. Hence we can conclude that volume is 3 dimensional. To measur…

    Read More

  2. 5th Grade Volume | Units of Volume | Measurement of Volume|Cubic Units

    Jul 20, 25 10:22 AM

    Cubes in Cuboid
    Volume is the amount of space enclosed by an object or shape, how much 3-dimensional space (length, height, and width) it occupies. A flat shape like triangle, square and rectangle occupies surface on…

    Read More

  3. Worksheet on Area of a Square and Rectangle | Area of Squares & Rectan

    Jul 19, 25 05:00 AM

    Area and Perimeter of Square and Rectangle
    We will practice the questions given in the worksheet on area of a square and rectangle. We know the amount of surface that a plane figure covers is called its area. 1. Find the area of the square len…

    Read More

  4. Area of Rectangle Square and Triangle | Formulas| Area of Plane Shapes

    Jul 18, 25 10:38 AM

    Area of a Square of Side 1 cm
    Area of a closed plane figure is the amount of surface enclosed within its boundary. Look at the given figures. The shaded region of each figure denotes its area. The standard unit, generally used for…

    Read More

  5. What is Area in Maths? | Units to find Area | Conversion Table of Area

    Jul 17, 25 01:06 AM

    Concept of Area
    The amount of surface that a plane figure covers is called its area. It’s unit is square centimeters or square meters etc. A rectangle, a square, a triangle and a circle are all examples of closed pla…

    Read More