**What Is Perpendicular?**

Two distinct lines intersecting each other at 90°, or a right angle, are called perpendicular lines.

**Example**:

Here, AB is perpendicular to XY because AB and XY intersect each other at 90°.

**Non-Example:**

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 Symbol

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.**

(a) | (b) |

(c) | (d) |

**Solution:**

- Parallel lines
- Perpendicular lines
- Perpendicular lines
- Parallel lines

**Example 2: Write a relation between the line segments indicated by the arrow in each shape.**

**Solution: **

- 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?**

**Solution:**

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.**

**Solution:**

## Practice Problems

## Perpendicular

### 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.