Perpendicular lines - Examples, Exercises and Solutions

Which lines are perpendicular to each other?

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.

Which lines are perpendicular to each other?

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.

Which figure shows perpendicular lines?

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.

Which of the figures shows parallel lines?

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.

Which of the figures show perpendicular lines?

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

What do the four figures below have in common?

All parallel

What can be said about the lines shown below?

Let's remember the different properties of lines.

The lines are not parallel since they intersect.

The lines are not perpendicular since they do not form a right angle of 90 degrees between them.

Therefore, no answer is correct.

None of the above.

Which lines are perpendicular to each other?

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.

Which of the lines are perpendicular to each other?

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.

Which of these lines are perpendicular to each other?

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.

Which lines are perpendicular to each other?

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.

All answers are correct.

Which of the diagrams shows perpendicular lines?

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.

What do the four figures have in common?

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.

How many pairs of perpendicular lines are there in the diagram?

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

The right angles we have in the drawing are:

$FAB,CDE$

The lines that create the angle FAB are: FA + AB

The lines that create the angle CDE are: CD + DE

Since we have 2 angles marked in the diagram, we therefore also have 2 pairs of perpendicular lines.

2

Are the diagonals of the given square perpendicular?

Let's remember that perpendicular lines are lines that intersect at a 90-degree angle.

According to the properties of the square, all angles measure 90 degrees and the diagonals are bisectors.

We will focus on the upper triangle formed by the diagonals intersecting each other.

Since all angles measure 90 degrees, the diagonals form two 45-degree angles.

We will draw this as follows:

Calculate the missing third angle in the triangle, marked with a question mark, as follows.

The sum of the angles of a triangle equals 180 degrees, so the formula to find the third angle is:

$180-45-45=$

$180-45=135$

$135-45=90$

Since the third angle equals 90 degrees, its complementary angle also equals 90 degrees:

Since the diagonals form a 90-degree angle between them, they are indeed perpendicular and perpendicular to each other.

Yes