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9.2: Intersecting and Parallel Lines

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Have you ever thought of designing your own skateboard park?

Marc and Isaac are working on a design for a new skateboard park. The city council of their town has agreed that the skateboard park is in need of renovation. Marc and Isaac have offered to help draw some initial plans to present at the next meeting. They are a little nervous about their design and about their presentation. Isaac’s mom offers to let them use some of her design paper and the two boys begin sketching their plan at the kitchen table.

“It definitely needs more rails,” Isaac says.

“What is a rail?” asks Isaac’s mom who glances at the design over her son’s shoulder.

“You know Mom, the sides don’t connect or cross,” Isaac says.

“Well, if that is what you want, your drawing is not accurate.”

Isaac looks down at the drawing. His mom is right. The rails don’t look correct.

To draw these rails, Isaac and Marc will need to understand the basics of Geometry. Pay attention to this Concept and you will understand how to help them with their design at the end.

Guidance

In the last Concept you learned about lines and line segments. When lines intersect, sometimes we need to describe how they do so. Two of the descriptions are intersecting lines and parallel lines .

Intersecting lines are lines that cross at some point. You can think of an intersection in a pair of streets to help you remember intersecting lines.

Here you can see that the streets of this highway intersect just as two intersecting lines intersect or cross. Here is an example of intersecting lines that you would see in geometry.

The lines intersect or cross at one point. We call this point the point of intersection . Sometimes lines will intersect with other lines at more than one point.

Parallel lines do not cross or intersect EVER. They are equidistant.

In the sport of gymnastics, gymnasts use parallel bars to perform. Notice that the parallel bars are two bars that do not connect. They are an equal distance apart and will never cross or intersect.

Here is what parallel lines in geometry look like.

If we use a symbol for parallel lines, the symbol looks like this: \overleftrightarrow{AB} \parallel \overleftrightarrow{CD} . This means that line AB is parallel to line CD .

Identify which lines are parallel and which are intersecting in each picture.

Example A

Solution: Parallel lines

Example B

Solution: Intersecting lines

Example C

Solution: Intersecting lines and parallel lines

Now let's go back to the skateboard park.

Have you figured out what is wrong with Isaac’s drawing? Think back to this Concept on geometry, reread the problem and underline any important information.

Marc and Isaac are working on a design for a new skateboard park. The city council of their town has agreed that the skateboard park is in need of renovation. Marc and Isaac have offered to help draw some initial plans to present at the next meeting. They are a little nervous about their design and about their presentation. Isaac’s mom offers to let them use some of her design paper and the two boys began sketching their plan at the kitchen table.

“It definitely needs more rails,” Isaac says.

“What is a rail?” asks Isaac’s mom, who glances at the design over her son’s shoulder.

“You know Mom, the sides don’t connect or cross,” Isaac says.

“Well, if that is what you want, your drawing is not accurate.”

Isaac looks down at the drawing. His mom is right. The rails don’t look correct.

If Isaac’s drawing is incorrect, then the rails in his drawing must not be parallel. Remember that parallel lines do not connect or cross in any way. When Isaac describes the rails to his mom it is clear that he wants them to be parallel. She says that his drawing is not accurate, so Isaac needs to redraw the rails and show that they do not connect.

Vocabulary

Here are the vocabulary words in this Concept.

Point
a location in space that does not have size or shape.
Ray
a line that has one endpoint and continues indefinitely in one direction.
Line
a set of connected points without endpoints.
Line Segment
a set of connected points with two endpoints.
Point of Intersection
the point where two intersecting lines meet.
Intersecting Lines
lines that cross or meet at some point
Parallel Lines
Lines that do not cross or meet EVER and are equidistant.

Guided Practice

Here is one for you to try on your own.

Look at this picture. Is the pattern made of parallel lines or intersecting lines?

Answer

This is a tricky question. The white tiles are definitely parallel to the opposite sides, but the lines do join at the corners with the brown square.

If you count the brown squares as part of the line, then they definitely do intersect.

If you don't count them, then the pattern is made up of parallel lines.

Many tile patterns are like this. Look around your home or school and you may find other patterns like this one.

Video Review

Here is a video for review.

James Sousa, Points, Lines, and Planes

Practice

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

1.

2.

3.

4.

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

5. Telephone wires

6. The yellow lines down a highway

7. Stitches on a sweater

8. The sides of a ramp

9. The tread on a stair

10. A spider web

11. A climbing web

12. The two sides of a trapeze

13. A trail in the mountains

Directions: Now go through a newspaper and find three examples of parallel lines and three examples of intersecting lines. Be sure to check your work with a friend.

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Date Created:

Oct 29, 2012

Last Modified:

Dec 17, 2014
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