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Intersecting and Parallel Lines

Define and identify intersecting and parallel lines.

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Intersecting and Parallel Lines

Credit: By Jmeddy at en.wikibooks [Public domain], from Wikimedia Commons
Source: https://commons.wikimedia.org/wiki/File%3AParallel_lines.jpg
License: CC BY-NC 3.0

Carmelita lives on Market Street and her best friend lives on Merlin Street. She looks at their streets on a map and tries to redraw them on a sheet of paper. She draws two lines to represent the relationship between their streets. Are their streets represented by parallel or intersecting lines?

In this concept, you will learn about intersecting lines and parallel lines.

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 is an example of intersecting lines that you would see in geometry.

The lines intersect at one point. This point is called the point of intersection. Sometimes lines intersect with other lines at more than one point.

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

Here is an example of parallel lines.

Credit: By Jmeddy at en.wikibooks [Public domain], from Wikimedia Commons
Source: https://commons.wikimedia.org/wiki/File%3AParallel_lines.jpg
License: CC BY-NC 3.0

If you use a symbol for parallel lines, the symbol looks like this: ABCD.

This means that line AB is parallel to line CD.

Examples

Example 1

Earlier, you were given a problem about Carmelita and her drawing of two streets.

Are the two streets represented by parallel or intersecting lines?

First, determine if the lines intersect.

No

Next, determine if the lines appear to be equidistant.

Yes

Then, identify the lines as parallel or intersecting.

Parallel

The answer is that the lines are parallel.

Example 2

Determine if the lines are parallel or intersecting.

License: CC BY-NC 3.0

First, determine if the lines intersect.

No

Next, determine if the lines appear to be equidistant.

Yes

Then, identify the lines as parallel or intersecting.

Parallel

The answer is that the lines are parallel.

Example 3

Determine if the lines are parallel or intersecting.

 

License: CC BY-NC 3.0

First, determine if the lines intersect.

Yes

Then, identify the lines as parallel or intersecting.

Intersecting

The answer is that the lines are intersecting.

Example 4

 Determine if the lines are parallel or intersecting.

License: CC BY-NC 3.0

First, determine if the lines intersect.

Yes

Then, identify the lines as parallel or intersecting.

Intersecting

The answer is that the lines are intersecting.

Review

Tell whether each picture shows parallel or intersecting lines.

  1. Credit: pixabay.com
    Source: https://pixabay.com/en/transition-away-bridge-wood-188311/
    License: CC BY-NC 3.0
  2. Credit: pixabay.com
    Source: https://pixabay.com/en/transition-away-bridge-wood-188311/
    License: CC BY-NC 3.0
    [Figure6][Figure7]

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

  1. Telephone wires
  2. The yellow lines down a highway
  3. Stitches on a sweater
  4. The sides of a ramp
  5. The tread on a stair
  6. A spider web
  7. A climbing web
  8. The two sides of a trapeze
  9. A trail in the mountains

Review (Answers)

To see the Review answers, open this PDF file and look for section 9.2. 

Resources

 

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Vocabulary

Intersecting lines

Intersecting lines are lines that cross or meet at some point.

line

A line is a straight one-dimensional figure that extends forever in opposite directions.

line segment

A line segment is a part of a line that has two endpoints.

Parallel

Two or more lines are parallel when they lie in the same plane and never intersect. These lines will always have the same slope.

Point

A point is a location in space that does not have size or shape.

Point of Intersection

A point of intersection is the point where two intersecting lines meet.

Ray

A ray is a part of a line that has one endpoint and continues indefinitely in one direction.

Image Attributions

  1. [1]^ Credit: By Jmeddy at en.wikibooks [Public domain], from Wikimedia Commons; Source: https://commons.wikimedia.org/wiki/File%3AParallel_lines.jpg; License: CC BY-NC 3.0
  2. [2]^ Credit: By Jmeddy at en.wikibooks [Public domain], from Wikimedia Commons; Source: https://commons.wikimedia.org/wiki/File%3AParallel_lines.jpg; License: CC BY-NC 3.0
  3. [3]^ License: CC BY-NC 3.0
  4. [4]^ License: CC BY-NC 3.0
  5. [5]^ License: CC BY-NC 3.0
  6. [6]^ Credit: pixabay.com; Source: https://pixabay.com/en/transition-away-bridge-wood-188311/; License: CC BY-NC 3.0
  7. [7]^ Credit: pixabay.com; Source: https://pixabay.com/en/transition-away-bridge-wood-188311/; License: CC BY-NC 3.0

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