Perpendicular
Two distinct lines which intersect at each other at 90° are called perpendicular lines. 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°. 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°. If two lines \(\overline{AB}\) and \(\overline{CD}\) are perpendicular to each other, we represent it using the notation \( \mathbf{ \overline{AB} \perp \overline{CD}}\).
Some shapes which have perpendicular lines are:
Properties of Perpendicular Lines
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 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 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 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 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.
Solved Examples
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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.
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°.
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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 can write: 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 and touch each other.
What are Perpendicular Angles?
Perpendicular angle can be referred to as the right angle (90°) that is formed when two perpendicular lines 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.
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.