Properties, Examples | Perpendicular Lines - Cuemath

Perpendicular Line

Perpendicular lines are the two distinct lines that intersect each other at 90°. Have you noticed anything common between the joining corners of your walls, or the letter 'L'? They are the straight lines known as perpendicular lines that meet each other at a specific angle - the right angle.

We say that a line is perpendicular to another line if the two lines meet at an angle of 90°. Let us understand the concept of perpendicular lines, the perpendicular sign, the difference between parallel and perpendicular lines, along with some perpendicular lines examples.

1.	What is Perpendicular?
2.	What are Perpendicular Lines?
3.	Properties of Perpendicular Lines
4.	How to Draw Perpendicular Lines?
5.	Perpendicular and Parallel Lines
6.	FQAs on Perpendicular

What is Perpendicular?

A perpendicular is a straight line that makes an angle of 90° with another line. 90° is also called a right angle and is marked by a little square between two perpendicular lines as shown in the figure given below. Here, the two lines intersect at a right angle, and hence, are said to be perpendicular to each other.

Now, let us look at the examples of lines that are not perpendicular. These lines are either not meeting at all, or intersecting at an angle that is not 90°. Hence, they are not perpendicular.

What are Perpendicular Lines?

Perpendicular lines, in math, are two lines that intersect each other and the angle between them is 90°.

Perpendicular Sign

When two lines are perpendicular, we express them using a perpendicular sign \(\mathbf{\perp}\). For example, if line \(\overline{AB}\) is perpendicular to line \(\overline{CD}\), we express it as \( \mathbf{ \overline{AB} \perp \overline{CD}}\).

Perpendicular Shapes

Perpendicular Shapes are those shapes that have at least two sides that join to form an angle of 90°. These are the shapes that have perpendicular lines in them. A few of them are:

• Square
• Right-angled triangle
• Rectangle

Properties of Perpendicular Line

We have already seen how the perpendicular lines look like. If there is an 'L' shape in a figure, the corresponding angle at the vertex is a right angle. Perpendicular lines always intersect each other, however, all intersecting lines are not always perpendicular to each other. The two main properties of perpendicular lines are:

• Perpendicular lines always meet or intersect each other.
• The angle between any two perpendicular lines is always equal to 90°

How to Draw Perpendicular Lines?

To draw a perpendicular line, all we need is a scale (ruler), a compass, or a protractor. We will discuss how to draw perpendicular lines step by step using a compass and a protractor. So, we can draw perpendicular lines for a given line in two ways.

• Using a protractor
• Using a compass

Drawing a Perpendicular Line Using Protractor

A protractor, in math, is considered an important measuring instrument in the geometry box. This tool not only helps us measure an angle in degrees, but also helps in drawing perpendicular lines. To draw a perpendicular line at point P on the given line, follow the steps given below.

• Step 1: Place the baseline of the protractor along the line such that its center is at P.
• Step 2: Mark a point B at 90° of the protractor.

• Step 3: Remove the protractor and join P and B. So, BP is a line that is perpendicular to the given line.

Drawing a Perpendicular Line Using Compass

We can also draw a perpendicular line using a compass. To draw a perpendicular line at a point P on a line, follow the steps given below.

• Step 1: Adjust the compass to the desired radius.
• Step 2: Placing the pointer of the compass at P, construct a semi-circle that cuts the line at A and B.

• Step 3: Without disturbing the radius of the compass, draw two arcs that cut the semi-circle at C and D by placing the pointer of the compass at A and B respectively.

• Step 4: Keeping the same radius, draw two intersecting arcs that intersect at Q by placing the pointer of the compass at C and D.

• Step 5: Join P and Q, which forms a perpendicular on the given line. Now, PQ is perpendicular to AB.

Perpendicular and Parallel Lines

Two straight lines are said to be parallel if they are equidistant from each other and never meet, no matter how much they may be extended in either directions. Observe the lines shown below to see the difference between perpendicular lines and parallel lines. In the figure, AB is perpendicular to CD and PQ is parallel to RS.

The symbol used to show that the lines are parallel is ||, and we express it as: PQ || RS. You can find parallel lines all around you. For example, zebra crossings on the road or the opposite sides of your ruler, and many others too! The table shown below differentiates between parallel lines and perpendicular lines.

Difference Between Parallel and Perpendicular Lines

The following table shows the main difference between parallel and perpendicular lines.

Parallel Lines	Perpendicular lines
Parallel lines are those lines that do not intersect anywhere and are always the same distance apart.	Lines that intersect each other forming a right angle are called perpendicular lines.
Example: the steps of a straight ladder; the opposite sides of a rectangle.	Example: the corner of two walls; the letter 'L'
The symbol used to denote two parallel lines: ||	The symbol used to denote two perpendicular lines: \(\mathbf{\perp}\).

☛ Related Articles:

• Perpendicular Lines Formula
• Perpendicular Line Calculator
• Perpendicular Bisector Theorem