Perpendicular Lines - Examples, Exercises and Solutions

Perpendicular lines are vertical lines that form a right angle between them, that is, an angle of $90°$ degrees.
Perpendicular lines appear in many geometric shapes, such as a rectangle, a square, a right triangle, and others.

Examples with solutions for Perpendicular Lines

Exercise #1

What do the four figures below have in common?

All parallel

Exercise #2

What do the four figures have in common?

Step-by-Step Solution

Remember that perpendicular lines form a 90-degree angle between them.

Parallel lines are lines that never intersect and do not form any angle between them.

To be able to examine the lines, a line will be drawn at each end of the line, as follows:

We notice that from the drawings it seems that all the lines do not form any angle between them, this is because they do not meet each other.

Therefore, all figures show parallel lines.

All show parallel lines.

Exercise #3

Which of the lines are perpendicular to each other?

Step-by-Step Solution

Let's remember that perpendicular lines are lines that form a right angle of 90 degrees between them.

In each of the answers, we will draw the letter T at the point of intersection of the lines.

Let's examine figure A:

We will notice that the lines do not form a right angle, and therefore are not perpendicular.

Let's examine figure B:

The lines do indeed form a 90-degree angle and are therefore perpendicular.

Let's examine figure C:

We notice that the lines do not form a right angle, and therefore are not perpendicular.

Exercise #4

Which lines are perpendicular to each other?

Step-by-Step Solution

Let's remember that perpendicular lines are lines that form an angle of 90 degrees between them.

In each of the answers, we will draw the letter T at the point of intersection of the lines.

Let's examine figure A:

We notice that the lines do form a right angle and the lines are perpendicular to each other.

Let's examine figure B:

We notice that the lines do not meet and do not form any angle; therefore, they are parallel lines and not perpendicular.

Exercise #5

Which lines are perpendicular to each other?

Step-by-Step Solution

Perpendicular lines are lines that form a right angle of 90 degrees between them.

The only drawing where the lines form a right angle of 90 degrees between them is drawing A.

Exercise #6

Which lines are perpendicular to each other?

Step-by-Step Solution

Let's remember that perpendicular lines are lines that form a right angle of 90 degrees between them.

The only drawing where it can be seen that the lines form a right angle of 90 degrees between them is drawing A.

Exercise #7

Which figure(s) show intersecting lines?

Step-by-Step Solution

Lines that intersect each other are lines that divide the side into two equal parts.

The drawings showing that the lines divide the sides into equal parts are drawings 1+3.

In drawing 2, the lines are perpendicular and vertical to each other, and in drawing 4, the lines are parallel to each other.

1 and 3

Exercise #8

Which of the figures show perpendicular lines?

Step-by-Step Solution

Perpendicular lines are lines that form a right angle of 90 degrees between them.

It can be observed that in figures 1 and 3, the angles formed by the lines between them are right angles of 90 degrees.

1 and 3

Exercise #9

Which lines are perpendicular to each other?

Step-by-Step Solution

Let's remember that perpendicular lines form a 90-degree angle with each other.

To check if the lines form a 90-degree angle, we will draw a T at each intersection as follows:

We notice that in each of the four drawings, the lines form a 90-degree angle.

Therefore all are correct as all the lines are perpendicular to each other.

Exercise #10

What do the 4 figures below have in common?

Step-by-Step Solution

Let's think about the different definitions of various lines.

We can see that what is common to all lines is that they intersect with each other, meaning they have a point of intersection.

We'll remember that lines that cross each other are lines that will meet at a certain point.

Therefore, the correct answer is a.

All intersections

Exercise #11

Which of the diagrams shows perpendicular lines?

Step-by-Step Solution

Let's remember that perpendicular lines form a 90-degree angle between them.

To check if the lines form a 90-degree angle, for each of the drawings a T is drawn at the intersecting point of the lines.

Let's examine figure A:

Note that the lines do not form a right angle.

Let's examine figure B:

We notice that the lines form a 90-degree angle and therefore are perpendicular.

Let's examine figure C:

Note that the lines do not form a right angle.

Let's examine figure D:

Note that the lines do not form a right angle.

Exercise #12

Which of these lines are perpendicular to each other?

Step-by-Step Solution

Let's remember that perpendicular lines form a 90-degree angle.

In each of the answers, we will draw the letter T at the intersection point of the lines.

Let's examine figure A:

We notice that the lines do not form a right angle and therefore are not perpendicular.

Let's examine figure B:

We notice that the lines do not form a right angle and therefore are not perpendicular.

Let's examine figure C:

We notice that the lines do not form a right angle and therefore are not perpendicular.

Let's examine figure D:

We notice that the lines do form a right angle therefore are perpendicular lines.

Exercise #13

Which lines are parallel to each other?

Step-by-Step Solution

Let's remember that parallel lines are lines that, if extended, will never intersect.

In diagrams a'+b'+c', all the lines intersect with each other at a certain point, except for diagram d'.

The lines drawn in answer d' will never intersect.

Exercise #14

Which figure shows perpendicular lines?

Step-by-Step Solution

Perpendicular lines are lines that form a right angle between them.

In the drawings A+C+D, you can see that the angles formed are not right angles.

It is possible to point out a right angle in drawing B.

Exercise #15

Which of the figures shows parallel lines?

Step-by-Step Solution

Parallel lines are lines that, if extended, will never meet.

In the drawings A+B+D if we extend the lines we will see that at a certain point they come together.

In drawing C, the lines will never meet, therefore they are parallel lines.