Perpendicular
Two distinct lines which intersect at each other at 90° are called perpendicular lines. Have you noticed anything common among the adjacent edges of a rectangular tabletop or the joining corners of your walls, or the letter "L"? They're 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 or a plane if it meets the line or the plane making an angle of 90^{°}. In this section, we will explore the world of perpendicular. The journey will take us through perpendicular angles, perpendicular sides, perpendicular examples, perpendicular shapes, and other interesting facts about the topic. So, let's get started to know more about them!
1.  What is Perpendicular? 
2.  Perpendicular Lines 
3.  Properties 
4.  How to Draw Perpendicular Lines? 
5.  Perpendicular and Parallel Lines 
What is Perpendicular?
A perpendicular is a 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. Here, the two lines intersect at a right angle, and hence, are said to be perpendicular to each other.
Now, look at the examples of lines that are not perpendicular. These lines are either not meeting at all, or intersecting at an angle which is NOT 90^{°}. Hence, they are NOT perpendicular.
Perpendicular Lines
Perpendicular lines, in math, are two lines that intersect each other and the angle between them is 90°. The symbol used in between the two lines to say that they are perpendicular is \( \mathbf{\perp}\). If two lines \(\overline{AB}\) and \(\overline{CD}\) are perpendicular to each other, we represent it using the notation \( \mathbf{ \overline{AB} \perp \overline{CD}}\).
There are some reallife examples of objects which have perpendicular lines in them. You can spot the perpendicular lines around you. Perpendicular shapes, in geometry, refer to shapes that include perpendicular lines. Some shapes which have perpendicular sides are:
 Square
 Rightangled triangle
 Rectangle
Properties of Perpendicular Lines
Now, you 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, you don't need any measurements. All you need is just a compass or a protractor. We will discuss how to draw the 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 Using a 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 mentioned below.
 Step 1: Place the baseline of the protractor along the line such that its center is at P.
 Step 2: Mark a point or a dot 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 Using a 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 mentioned below.
 Step 1: Adjust the compass to the desired radius.
 Step 2: Placing the pointer of the compass at P, construct a semicircle that cuts the line at A and B.
 Step 3: Without disturbing the radius of the compass, draw two arcs that cut the semicircle 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.
Perpendicular and Parallel Lines
Two straight lines are said to be parallel if they are equidistant (at an equal distance) from each other and never meet, no matter how much they may be extended in either direction. Observe the lines to see that AB is parallel to CD and PQ is parallel to RS.
The symbol used to show that the lines are parallel is , and we express it this way: AB \(\perp\) CD and 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.
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: \(\mathbf{\perp}\). 
Solved Examples

Example 1:
The two lines inside the kite intersect each other at right angles. List the total number of right angles formed at the intersection and name the pair of perpendicular lines.
Solution
Since the two lines AB and CD intersect each other at right angles, there are 4 right angles at the intersecting point. Hence, Angle AOD = Angle DOB = Angle BOC = Angle AOC = 90^{°}. So, AB is perpendicular to CD.

Example 2:
In the following figure, AB is perpendicular to CD. If Angle BOC = 90^{°}, then find the value of x.
Solution
Since Angle BOC = 90^{°}, we have: x + 63 = 90. Therefore, x = 27°
Practice Questions
FAQs on Perpendicular
What is the Difference Between Perpendicular and Parallel Lines?
Perpendicular lines are those lines that intersect each other at right angles (90°). Parallel lines are those lines that do not intersect anywhere and are always the same distance apart.
What is Perpendicular in English?
Perpendicular, in English, means standing at right angles to the plane of the horizon.
Do Perpendicular Lines Touch Each Other?
Yes, one of the properties of perpendicular lines is that they intersect or pass through each other.
What Are Perpendicular Angles?
Perpendicular angles can be referred to as right angles (90°) that two perpendicular lines form when they intersect each other.
How do You Know if Two Lines Are Perpendicular?
If two lines intersect each other making an angle of 90°, then those two lines are perpendicular to each other. Another important property used to determine perpendicular lines is that the product of the slope of one line and the reciprocal slope of the other line is always 1.
Are Diagonals of a Rhombus Perpendicular to Each Other?
The diagonals of a rhombus intersect each other at an angle of 90°, so we can say that the diagonals of a rhombus are perpendicular to each other.