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Lines are one of the most basic and fundamental shapes in geometry. They form the basics of almost all the figures in geometry. There are many types of lines and one such line is the perpendicular line.
Let’s understand what is a perpendicular line in geometry and its properties with examples.
What is a Perpendicular Line in Geometry?
A perpendicular is a straight line that makes an angle of $90^{\circ}$ with another line. $90^{\circ}$ 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.
Define Perpendicular Lines in Geometry
In geometry perpendicular lines, are two lines that intersect each other and the angle between them is $90^{\circ}$. If two lines $\overleftrightarrow{AB}$ and $\overleftrightarrow{CD}$ are perpendicular to each other, we represent it using the notation $\overleftrightarrow{AB} \perp \overleftrightarrow{CD}$.
Examples of shapes formed by perpendicular lines are rectangles, squares, and right-angled triangles.
Examples of Non-Perpendicular Lines
Following are examples of non-perpendicular lines.
The two lines are parallel and do not intersect each other. They can never be perpendicular to each other.
The two lines are intersecting each other at an angle, not $90^{\circ}$. So, they are not perpendicular.
Note:
- Such lines are called intersecting lines.
- All perpendicular lines are intersecting lines, but not all intersecting lines are perpendicular lines.
- Two intersecting lines are called perpendicular lines, only if they make an angle of $90^{\vcirc}$.
Properties of Perpendicular Lines
The following are the properties of perpendicular lines
- Perpendicular lines always intersect at right angles
- If two lines are perpendicular to the same line, they are parallel to each other and will never intersect
In the above figure $l \perp m$ and $l \perp n$, therefore, $m || n$.
Real-Life Examples of Perpendicular Lines
Some real-life examples of perpendicular lines are
- The hands of a clock at 3.00 a.m. or 3.00 p.m.
- Corners of your school blackboard
- Corners of geometrical instruments such as a ruler, and set-squares.
- Corners of doors and windows of your house.
Difference Between Perpendicular Lines and Parallel Lines
The following are the differences between perpendicular lines and parallel lines.
| Perpendicular Lines | Parallel Lines |
| Lines that intersect each other forming a right angle are called perpendicular lines | Parallel lines are those lines that do not intersect anywhere and are always the same distance apart |
| The symbol used to denote two perpendicular lines is $\perp$ | The symbol used to denote two parallel lines is || |
Example: The corners of the notebook | Example: Railway tracks |
Practice Problems
- State True or False
- Angle between two perpendicular lines is $0^{\circ}$
- Angle between two perpendicular lines is $90^{\circ}$
- All intersecting lines are perpendicular lines
- All perpendicular lines are intersecting lines
- Two perpendicular lines can be parallel also
- Two perpendicular lines can never be parallel
- Two lines perpendicular to the same line are parallel to each other
- Two lines perpendicular to the same line are perpendicular to each other
- At what time the hands of the clock will be perpendicular to each other?
- 12 o’clock
- 6 o’clock
- 9 o’clock
- 5 o’clock
FAQs
What are perpendicular lines?
Lines that intersect each other at $90^{\circ}$ are called perpendicular lines.
Do perpendicular lines meet (intersect)?
Yes, perpendicular lines always intersect at right angles $\left(90^{\circ} \right)$.
What is the difference between perpendicular lines and parallel lines?
Perpendicular lines intersect at right angles $\left(90^{\circ} \right)$ while parallel lines are parallel to each other and never intersect.
Are all intersecting lines always perpendicular?
No, not all intersecting lines are perpendicular to each other. They may intersect at different angles other than $90^{\circ}$.
Conclusion
Two lines that intersect each other at right angles $\left( 90^{\circ}\right)$ are called perpendicular lines. The perpendicular lines are an important concept in geometry. The adjacent edges (or sides) of figures like rectangles, squares, and right-angled triangles are perpendicular lines.
