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!

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, 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 real-life 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
• Right-angled triangle
• Rectangle 

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 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.

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.

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.