What Is Perpendicular?
Here, AB is perpendicular to XY because AB and XY intersect each other at 90°.
|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 acute angle. So, they are not perpendicular.||The lines are not intersecting each other at right angles.|
Perpendicular lines are represented by the symbol ‘⊥’. Suppose, m and n are two lines intersecting each other at 90°, then they are perpendicular to each other and are represented as m ⊥ n. The point of intersection of perpendicular lines is called the foot of the perpendicular.
Properties of Perpendicular Lines
- These 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.
- Adjacent sides of a square and a rectangle are always perpendicular to each other.
- The sides of the right-angled triangle enclosing the right angle are perpendicular to each other.
Real Life Examples
We can observe many perpendicular lines in real life.
Some examples are the sides of a set square, the arms of a clock at certain times of the day, the corners of the blackboard, a window, and the Red Cross symbol.
Difference between Perpendicular Lines and Parallel Lines
|Perpendicular Lines||Parallel Lines|
|Perpendicular lines are lines that intersect at a 90° angle.||Parallel lines are lines that are always the same distance apart. Parallel lines never intersect.|
|The symbol used to represent a perpendicular line is “⊥”.||The symbol used to represent a parallel line is “||”.|
|Example: The corner of the postcard||Example: Railway tracks|
|The corner of a ruler||The edges of a ruler|
Construction of Perpendicular Lines
We can draw perpendicular lines for a given line in two ways.
- Using a protractor
- Using a compass
Drawing a perpendicular line using a protractor
Step 1: Let m be the given line and A the given point on it.
Step 2: Place the protractor on the line m such that its baseline coincides with m, and its center falls on A.
Step 3: Mark a point B against the 90-degree mark on the protractor.
Step 4: Draw a line n passing through A and B.
Then line m ⊥ line n at A.
Drawing a perpendicular line at a given point on a line using a compass
Step 1: Place a compass tip on the given point A. Take an appropriate radius and draw an arc on either side of the given point.
Step 2: Stretch the compass wider. Place the compass tip on the new points and make a small arc above the given line. The two new arcs will intersect.
Step 3: Use the ruler to join the given point A and point B where the arcs intersect.
Solved Examples on Perpendicular
Example 1: State whether a given set of lines are perpendicular or parallel.
- Parallel lines
- Perpendicular lines
- Perpendicular lines
- Parallel lines
Example 2: Write a relation between the line segments indicated by the arrow in each shape.
- AB ⊥ AE
- PQ || SR
- PQ || NM
- AB ⊥ AD
Example 3: The diagonals of a rhombus are perpendicular to each other. How many right angles are formed at the intersection?
Since the lines AC and BD intersect each other at 90 degrees, there are 4 right angles at the intersecting point.
∠AED = ∠DEC = ∠CEB = ∠BEA = 90 degrees
Example 4: Name some two-dimensional shapes that have perpendicular lines.
Identify the pair of perpendicular line segments in a given shape.
FE and ED are perpendicular line segments.
Each object has a highlighted pair of lines. Which of this object highlighted pair of lines does not show perpendicular lines?
Candle. Its highlighted pair of lines shows parallel lines.
At what time the hands of the clock will be perpendicular to each other?
At 3 o’clock the hands of the clock are at 90 degrees to each other. So they are perpendicular to each other.
How many lines are perpendicular to line CD in a given figure?
Line PQ, line RS and line TU are perpendicular to CD. So, there are 3 lines perpendicular to line CD in the given figure.
Frequently Asked Questions
What are perpendicular lines?
Perpendicular lines are those lines that intersect each other at 90 degrees.
Do perpendicular lines have to meet?
These lines always intersect at right angles.
What is the perpendicular symbol?
The perpendicular symbol is ⊥. It is used between the two lines to show that they are perpendicular to each other.
What is the difference between perpendicular lines and parallel lines?
Perpendicular lines intersect at right angles (90°) 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 degrees.