Perpendicular Lines

7 min read
Perpendicular Lines

What Are Perpendicular Lines?

You are riding your bike down the street. You must be careful because you must cross another street. Another street intersects your street. These streets are perpendicular.

Perpendicular lines are lines that intersect each other. In math, you may find that lines are either perpendicular or parallel. Below is a set of lines that are perpendicular.

two perpendicular lines

Lines may only be considered perpendicular if they meet certain rules. Let’s look at these rules.

Perpendicular Rules

  • Two lines must be involved.
  • The two lines must cross.
  • The angles must be at 90 degrees.

2 perpendicular lines

Therefore, in the picture above, you can tell that these lines are perpendicular. They follow the rules from above. The symbol that looks like а square means that the angle measures 90 degrees.

This means that the angle makes а perfect square. Each angle will make а perfect square and measure 90 degrees if one of the angles is а perfect square.

lf that symbol was not there, then you must measure the angle.

So, there are two lines involved, and they cross. One line must bе а vertical line, and the other line must bе а horizontal line.

Now, they must form а right angle, which it does based on the symbol. Therefore, these are perpendicular lines.

Keep in mind that not all lines that intersect are perpendicular. Some lines intersect at different angles.

lf you look at the lines below, they show two lines that intersect. However, you can tel1 that they do not make а perfect square or right angle at 90 degrees.

So, these lines may intersect, but these lines are not perpendicular.

meaning of perpendicular lines in mathematics

How To Form Perpendicular Lines

If your teacher asked you to draw perpendicular lines, that might sound like an easy thing to do. However, it takes a few steps to actually create lines that are truly perpendicular.

Remember, you can’t just draw two lines in which one lines crosses over the other. Instead, the angles must be perfect squares or perfect right angles.

Let’s look at the lines below. Those were drawn without any tools. The person who drew these lines was told to draw perpendicular lines, so he did. Are those actually perpendicular lines? Looks can be deceiving.

The only way to make sure that these lines are perpendicular is to make sure that they follow the rules. First, there are two lines, and they cross or intersect. The most important part is that the angle is 90 degrees.

We would need to measure each angle to make sure. However, if you look closer, you may see that the line dips down slightly on the right which probably means that it is not a straight line, so it would not make a right angle.

perpendicular lines on a graph

Therefore, you will need a few school tools to make a set of perpendicular lines. First, you need a protractor to measure the right angles. You probably have seen a protractor before.

Second, you may need a ruler or straight edge to make sure that the lines are straight. If you don’t want to erase a lot (which I recommend), you can also use a compass instead.

Compasses are used to help you draw lines that form certain angles. The compass is not the type you have in your hand while hiking that points you in the right direction.

Instead, this compass is the one you use in math. It holds a pencil. If you don’t use a compass, you might have to erase your lines several times to make sure they are at the right angle.

The pictures below show these tools.

Follow these steps below to make perfect perpendicular lines. Use the picture and labels to help you out.

finding perpendicular line

  1. With your straight edge or ruler, draw a straight horizontal line.
  2. Draw a dot in the middle of your line. This part does not have to be exact.
  3. Put your compass point on the dot and draw a small circle completely around the dot using the compass.
  4. Next, place your compass point on the part of the circle that touches the line (A). Open the compass a little further and draw an arc above the circle.
  5. Place the compass point on the other side of the circle that touches the line (B). Draw another arc, so that it intersects with your other arc.
  6. Draw a dot where the arcs intersect.
  7. Last, using your straight edge, draw a vertical line from the dot in the arc down through the horizontal line. Now, you have perfect perpendicular lines.

angles and perpendicular lines

Using Perpendicular Lines In The Real World

Perpendicular lines are everywhere. You probably have never noticed them. This means that someone measured to make sure that the angles are at right angles, and the lines are completely straight.

Look at a bookcase. It has perpendicular lines. The black lines show that it is perpendicular.

Why do you think a bookcase would have to have perpendicular lines? If they didn’t, the books would be leaning.

They would not be standing straight up. You could also place more books on the shelves if they are standing straight.

examples of perpendicular lines in real life

Think about where else you would find perpendicular lines. How about a floor and wall in a house? A floor would need to be straight as well as the wall.

What would happen if the floor was slanted?

Then objects would roll. The walls need to be straight too. The only way to do this is for both the wall and floor to be perpendicular. In the picture below, see if you can find the perpendicular lines.

example of perpendicular lines in our surroundings

The perpendicular lines are across and down the far wall. We see perpendicular lines everywhere. Your television and a frame of artwork in your house all have perpendicular lines.

Let’s see if you can see whether a set of lines are perpendicular. You will need a protractor to measure the angles or you can use the corner of something like a sheet of paper or cover of a book because you know that these already have right angles.

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