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8.5: Parallel and Perpendicular Lines

Difficulty Level: Basic Created by: CK-12
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Have you ever explored lines at an art museum? Take a look at what Mrs. Gilson's class discovered.

While looking at this painting, the students in Mrs. Gilson's class began to talk about lines.

"I can see a lot of intersecting lines," Jonas commented.

"Not only that, but some are parallel," Corinna added.

"Perpendicular too," Jonas continued.

All three types of lines are present in this painting.

Can you identify them?

This Concept will teach you how to identify parallel, intersecting and perpendicular lines. When finished, you will know how to answer this question.

Guidance

What about the relationship between different types of lines? We have been working with intersecting lines and with the angle relationships that are formed by them, but there are other types of line relationships. Let’s look at them now.

What do we know about lines?

Lines exist in space. Two lines intersect when they cross each other. Because all lines are straight, intersecting lines can only cross each other once. Look at the examples below. Imagine the lines extend beyond the picture, on forever. Can you see how they will never cross more than once?

Two lines that form right angles when they intersect are perpendicular lines. All four angles formed by the perpendicular lines measure 90^\circ . We use a small box to show a right angle. If any of the four angles is marked with the small box, we know the lines are perpendicular. Take a look at the perpendicular lines below.

Some lines never intersect. We call these parallel lines. Parallel lines never cross, so they do not form any angles. Parallel lines look like railroad tracks; they are always the same distance apart, running next to each other.

One easy way to remember the difference between parallel and perpendicular lines is to look at the l’s in parallel. Parallel lines look exactly like the two l’s in their name!

Identify whether the pairs of lines are parallel, perpendicular, or just intersecting.

As you look at each pair, first decide whether they intersect or if they might intersect if the lines were extended. If they do not or will not intersect, they must be parallel.

The lines in Figure 1 do not intersect. Let’s double check. Do they look like railroad tracks or the l’s in parallel? They do. The lines are always the same distance apart. No matter how far we extend them, they will never intersect. Figure 1 therefore shows parallel lines.

The rest of the pairs show intersecting lines. But which pairs are perpendicular? Remember, perpendicular lines form right angles when they intersect. If the two lines are too slanted, as in Figure 2, they cannot form right angles. Also, look for the little box that tells when an angle is a right angle. Let’s look at each of the pairs.

As we’ve said, the lines in Figure 2 are very slanted. They do not form perfect corners, or right angles, when they cross. They are intersecting lines, but not perpendicular lines.

The lines in Figure 3 do form right angles. The small box tells us that the lines definitely form right angles, so these are perpendicular lines.

Now let’s look at the lines in Figure 4. They do not intersect! But remember, lines continue in both directions forever. What would happen if we extend each line? Trace each with your finger. Will they cross if you extend them? They sure will. Now imagine what they will look like when they intersect, or draw a picture to help you. Would they meet at a slanted angle, or would they form right angles?

These lines do not form right angles, so they cannot be perpendicular. They are intersecting lines only.

Here are a few to try on your own. Identify each pair of lines are parallel, intersecting or perpendicular.

Example A

Solution: Intersecting Lines

Example B

Solution: Parallel lines

Example C

Solution: Parallel lines

Here is the original problem once again.

While looking at this painting, the students in Mrs. Gilson's class began to talk about lines.

"I can see a lot of intersecting lines," Jonas commented.

"Not only that, but some are parallel," Corinna added.

"Perpendicular too," Jonas continued.

All three types of lines are present in this painting.

Can you identify them?

If you notice the intersecting lines are lines that cross at some point, or will cross if they were to continue.

Parallel lines will never cross.

Perpendicular lines intersect to form right angles.

Make notes of all three lines in this painting. Then work with a partner and compare your answers. Discuss any differences.

Vocabulary

Intersecting Lines
lines that cross at one point.
Parallel Lines
lines that will never cross.
Perpendicular Lines
lines that intersect at a right angle.
Corresponding Angles
angles that are in the same place in each intersection when a line crosses two parallel lines.

Guided Practice

Here is one for you to try on your own.

What type of lines are best described in this picture?

Answer

The streets of this highway form intersecting lines. We can be even more specific. If you look at the lines that form the cross shape in the highway, these lines are also perpendicular because right angles are formed.

Video Review

This Khan Academy video is on parallel and perpendicular lines.

Practice

Directions: Use what you have learned to answer each question true or false.

1. Adjacent angles are also supplementary angles.

2. Vertical angles are complementary angles.

3. If one adjacent angle is 100^\circ , then its angle pair is also 100^\circ .

4. Vertical angles have the same measure.

5. Vertical angles and corresponding angles are located in the same position.

6. You can have corresponding angles when you only have two intersecting lines.

7. Corresponding angles are in the same place given the intersection.

8. Parallel lines will never intersect.

9. Perpendicular lines intersect at a 90 degree angle.

Directions: Tell whether each picture shows parallel or intersecting lines.

10.

11.

Directions: Think about each example described below and determine whether the lines would be intersecting or parallel.

12. Telephone wires

13. The yellow lines down a highway

14. Stitches on a sweater

15. The sides of a ramp

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Difficulty Level:

Basic

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Date Created:

Nov 30, 2012

Last Modified:

Jul 17, 2014
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