Perpendicular Lines: Identifying and defining elements

Examples with solutions for Perpendicular Lines: Identifying and defining elements

Exercise #1

Which lines are parallel to each other?

Video Solution

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.

Answer

Exercise #2

Which lines are perpendicular to each other?

Video Solution

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.

Answer

Exercise #3

Which lines are perpendicular to each other?

Video Solution

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.

Answer

Exercise #4

Which figure(s) show intersecting lines?

1234

Video Solution

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.

Answer

1 and 3

Exercise #5

Which figure shows perpendicular lines?

Video Solution

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.

Answer

Exercise #6

Which of the figures shows parallel lines?

Video Solution

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.

Answer

Exercise #7

Which of the figures show perpendicular lines?

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Video Solution

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.

Answer

1 and 3

Exercise #8

What do the four figures below have in common?

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Video Solution

Step-by-Step Solution

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

We can see that what all lines have in common is that they form a right angle of 90 degrees with each other.

Let's remember that lines that form a right angle of 90 degrees with each other are perpendicular and vertical lines.

Therefore, the correct answer is a.

Answer

All perpendicular

Exercise #9

What do the four figures below have in common?

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Video Solution

Step-by-Step Solution

Answer

All parallel

Exercise #10

What do the 4 figures below have in common?

1234

Video Solution

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.

Answer

All intersections

Exercise #11

What do the four figures below have in common?

1234

Video Solution

Step-by-Step Solution

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

We can see that what all these lines have in common is that they form a right angle of 90 degrees with each other.

Let's remember that lines that form a right angle of 90 degrees with each other are perpendicular and vertical lines.

Therefore, the correct answer is a.

Answer

All perpendicular

Exercise #12

What can be said about the lines shown below?

Video Solution

Step-by-Step Solution

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.

Answer

None of the above.

Exercise #13

Which lines are perpendicular to each other?

Video Solution

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.

Answer

Exercise #14

Which of the lines are perpendicular to each other?

Video Solution

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.

Answer

Exercise #15

Which of these lines are perpendicular to each other?

Video Solution

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.

Answer

Exercise #16

Which lines are perpendicular to each other?

1234

Video Solution

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:

1234We 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.

Answer

All answers are correct.

Exercise #17

Which of the diagrams shows perpendicular lines?

Video Solution

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.

Answer

Exercise #18

What do the four figures have in common?

1234

Video Solution

Step-by-Step Solution

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

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

In order to examine the types of angles that lines form with each other, we will draw a T at the intersection point of the lines in the following way:

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Note that from the drawings we can see that what they all have in common is the right angle, which means that all the lines are perpendicular.

Answer

All show perpendicular lines.

Exercise #19

What do the four figures have in common?

1234

Video Solution

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:

1234

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.

Answer

All show parallel lines.

Exercise #20

Which lines are perpendicular to each other?

1234

Video Solution

Step-by-Step Solution

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

To examine the types of angles that lines create with each other, let's draw a T at the intersection point of the lines in the following way:

1234

Note that in drawings 1+4 we see right angles, meaning the lines are perpendicular to each other.

In the other drawings, the angles created are greater or smaller than 90 degrees, therefore the lines are not perpendicular.

Answer

1 and 4