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Parallel and Perpendicular Lines

Parallel, perpendicular, and intersecting lines

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Identify Types of Lines
License: CC BY-NC 3.0

Candice saw the following illustration in her Math book.

License: CC BY-NC 3.0


She wondered how to describe the relationship between the brown plane and the green plane.

In this concept, you will learn to identify types of lines.

Parallel, Perpendicular and Intersecting Lines

Lines are around you everywhere and you see them every day. When you drive along a highway there are lines painted on the road indicating the width of the lane, lines painted indicating cross walks and lines indicating the intersection of roads. If you look up to the sky you often see lines that are vapor trails left by airplanes.

Although lines are a common occurrence in the real-world, they are special and have names. The lines painted on the road indicating the width of the driving lane are parallel lines. Parallel lines are two lines on a plane that never meet and remain the same distance over their entire length. The following diagrams show pairs of parallel lines:

License: CC BY-NC 3.0

License: CC BY-NC 3.0

The arrows on the lines show that the lines are parallel to each other. When naming lines that are parallel, the symbol \begin{align*}\parallel \end{align*} is used.

Straight lines that are at right angles to each other are called perpendicular lines. These lines meet each other such that a 90° angle is formed. When a Cartesian grid is drawn, the \begin{align*}x\end{align*} and \begin{align*}y\end{align*} axes meet at right angles. When naming lines that are perpendicular, the symbol \begin{align*}\bot \end{align*} is used.

License: CC BY-NC 3.0

Straight lines that cross each other at some point are called intersecting lines. These lines will intersect at one point only over their entire length. There is no symbol to us when naming intersecting lines. The following diagram shows intersecting lines.

License: CC BY-NC 3.0

Examples

Example 1

Earlier, you were given a problem about Candice and the picture. She needs to describe the relationship between the two planes.

First, look at the two planes and write down what she knows from the picture.

The green plane and the brown plane are equidistant – the distance between them is equal over their entire length.

Next, figure out what this means with respect to the planes.

This means that the planes will never meet or intersect.

Then, state the relationship between the planes.

The planes are parallel.

Candice can now say that the green and brown planes in the picture are parallel.

Example 2

Name the type of lines represented by the following real-world situations:

i) Railroad tracks and overhead power lines.

ii) Diagonal distances from home plate to 2nd base and from 1st base to 3rd base of a baseball diamond.

iii) Solid double lines painted in the middle of a two-way road.

iv) Corners formed by the trim around a rectangular window.

v) Legs of an ironing board

Answers:

i) Railroad tracks and overhead power lines.

Parallel lines.

ii) Diagonal distances from home plate to 2nd base and from 1st base to 3rd base of a baseball diamond.

Perpendicular lines.

iii) Solid double lines painted in the middle of a two-way road.

Parallel lines.

iv) Corners formed by the trim around a rectangular window.

Perpendicular lines.

v) Legs of an ironing board.

Intersecting lines

Example 3

For the following regular trapezoid name, with proper symbols, one pair of parallel lines, one pair of intersecting lines and one pair of perpendicular lines.

License: CC BY-NC 3.0

Parallel Lines

First, review what you know about parallel lines.

-always the same distance apart

-never meet or intersect

-indicated with same arrows on the lines

Next, look at the diagram and find the pair of parallel lines

Lines \begin{align*}\overline{AB}\end{align*} and \begin{align*}\overline{CD}\end{align*} display an arrow.

Then, name the parallel lines using the correct symbol.

 \begin{align*}\overline{AB} \parallel \overline{CD}\end{align*} 

Intersecting Lines

First, review what you know about intersecting lines.

-intersect at one point only

-can intersect at any angle

-no indication marks

Next, look at the diagram and find the pair of intersecting lines.

\begin{align*}\overline{AD}\end{align*} and \begin{align*}\overline{BC}\end{align*}

Then, name the intersecting lines using the correct symbol.

\begin{align*}\overline{AD}\end{align*} intersects \begin{align*}\overline{BC}\end{align*}. There is no symbol to represent intersecting lines

Perpendicular Lines

First, review what you know about perpendicular lines.

-intersect or meet at one point only

-will meet or intersect at a 90° angle

-right angle is shown with a square

Next, look at the diagram and find the pair of intersecting lines.

\begin{align*}\overline{AE}\end{align*} and \begin{align*}\overline{CD} \end{align*}

Then, name the intersecting lines using the correct symbol.

\begin{align*}\overline{AE} \bot \overline{CD}\end{align*}.

Review

Name each type of lines shown below.

1. 

License: CC BY-NC 3.0

2. 

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3. 
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4. 

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Write the definitions for the following types of lines.

5. Parallel lines

6. Intersecting lines

7. Perpendicular lines

Answer the following questions about different types of lines.

8. What is the symbol for parallel lines?

9. What is the symbol for perpendicular lines?

10. An intersection on a highway is an example of what type of lines?

11. A four way stop is an example of what type of lines?

12. Is it possible for intersecting lines to also be considered perpendicular?

Describe the types of lines shown in each illustration.

13. 

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14. 

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15. 

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Review (Answers)

To see the Review answers, open this PDF file and look for section 6.3. 

Resources

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Vocabulary

Angle

A geometric figure formed by two rays that connect at a single point or vertex.

Intersecting lines

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

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.

Perpendicular lines

Perpendicular lines are lines that intersect at a 90^{\circ} angle.

Straight angle

A straight angle is a straight line equal to 180^{\circ}.

Image Attributions

  1. [1]^ License: CC BY-NC 3.0
  2. [2]^ 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]^ License: CC BY-NC 3.0
  7. [7]^ License: CC BY-NC 3.0
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  9. [9]^ License: CC BY-NC 3.0
  10. [10]^ License: CC BY-NC 3.0
  11. [11]^ License: CC BY-NC 3.0
  12. [12]^ License: CC BY-NC 3.0
  13. [13]^ License: CC BY-NC 3.0
  14. [14]^ License: CC BY-NC 3.0

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