Back To Course

Math 102: College Mathematics15 chapters | 122 lessons | 13 flashcard sets

Are you a student or a teacher?

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*DaQuita Hester*

DaQuita has taught high school mathematics for six years and has a master's degree in secondary mathematics education.

What are the different types of lines? Where are they visible in the real world and how can you recognize them? Find out here and test your knowledge with a quiz.

Take a look at your surroundings. Are you sitting at a desk? Are you close to a window with blinds? If you look out that window, can you see the next street or a highway? If you answered yes to any of these questions, then you are surrounded by lines, which are everywhere!

In this lesson, we are going to take a closer look at parallel lines, perpendicular lines and transverse lines. Each of these types of lines are classified as **coplanar** lines, meaning that they are located on the same plane, which is a flat, two-dimensional surface. Let's examine and practice with each one.

**Parallel lines** are defined as coplanar lines that do not intersect. They have the same slope and, just as the definition states, will never, ever meet at any point. Think about it: since slope is referred to as rise over run, having the same slope means that two lines will rise and run at the exact same rate, ensuring that they will never intersect each other. Let's take a look at real-life examples of parallel lines.

First, we have a window with blinds. Here, you can see that each blind is moving in the same direction and never touches another blind. Next, we have a parking lot. Notice that all of the lines are going in the same direction.

**Perpendicular lines** are coplanar lines that intersect and form a 90-degree angle. So, any time you have perpendicular lines, you will also have right angles and vice versa.

The slopes of perpendicular lines are **opposite reciprocals** of each other. Being opposite means that one slope will be positive and the other will be negative. Being reciprocals means that one slope will be the upside down or flipped version of the other.

Perpendicular lines are also visible in the real world. Take a look at a desk. Can you see how the top of it lays flat on all the legs? This means that the top of the desk is perpendicular to the legs and forms ninety-degree angles, which keeps things from sliding off of it.

Now, let's practice what we've learned so far. If line *g* = 3*x* + 7 and line *h* = -3*x* - 2, are these lines parallel, perpendicular or neither?

Let's begin by looking at their slopes, which are the numbers in front of the *x* variables. Line *g* has a slope of three and line *h* has a slope of negative three. Their slopes are the same number, but one is positive and the other is negative. so they are not exactly the same. For this reason, we know that line *g* is not parallel to line *h*. Also, though their slopes are opposites, they are not reciprocals of each other. Therefore, we can also conclude that these two lines are not perpendicular.

For our next example, line *j* = 4/3*x* + 2 and line *k* = -3/4*x* + 5. Are these two lines parallel, perpendicular or neither?

By looking in front of the *x* variables, we see that line *j* has a slope of four-thirds, and line *k* has a slope of negative three-fourths. These slopes are not congruent, so the lines cannot be parallel. However, one slope is positive and the other slope is negative. Additionally, these slopes are reciprocals or flipped fractions of each other. Therefore, we can conclude that the lines are perpendicular.

A **transversal** is a line that intersects two or more coplanar lines at different points. For example, in this figure, line *t* is a transversal because it intersects both line *a* and line *b*. Transversals have an important role in geometry because they are needed to form alternate interior angles, alternate exterior angles, consecutive interior angles and corresponding angles.

In the real world, transversals are highly visible on street maps. Take a look at this one. Here, you can see that Elm Street is a transversal to Asbury Street, W. Taylor Street and Villa Avenue.

Now, let's practice identifying a transversal. Take a look at the following scenario. Which line is the transversal?

Line *a* does not intersect any other line. Line *b* intersects line *c*. Line *c* intersects line *b* and line *d*, and line *d* intersects line *c*. Therefore, since a transversal must intersect at least two lines, we can conclude that line *c* is the transversal.

In review, remember that all of the lines we discussed are coplanar. Parallel lines have congruent slopes, perpendicular lines have opposite reciprocal slopes, and to be a transversal, a line must intersect at least two other lines at different points.

From office furniture to highway road maps, lines are everywhere. Whether parallel, perpendicular or transverse, lines provide structure for our everyday lives.

After finishing this lesson, you should be able to:

- Define coplanar lines
- Recognize the congruent slopes in parallel lines
- Remember that opposite reciprocal slopes are perpendicular lines
- Recall that you need at least two intersections to have a transversal line

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackDid you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
9 in chapter 14 of the course:

Back To Course

Math 102: College Mathematics15 chapters | 122 lessons | 13 flashcard sets

- Go to Logic

- Go to Sets

- Properties of Shapes: Rectangles, Squares and Rhombuses 5:46
- Properties of Shapes: Triangles 5:09
- Perimeter of Triangles and Rectangles 8:54
- Area of Triangles and Rectangles 5:43
- Circles: Area and Circumference 8:21
- The Pythagorean Theorem: Practice and Application 7:33
- How to Identify Similar Triangles 7:23
- Applications of Similar Triangles 6:23
- Parallel, Perpendicular and Transverse Lines 6:06
- Angles and Triangles: Practice Problems 7:43
- Properties of Shapes: Circles 4:45
- Go to Geometry

- Computer Science 332: Cybersecurity Policies and Management
- Introduction to SQL
- Computer Science 203: Defensive Security
- GRE Information Guide
- Computer Science 310: Current Trends in Computer Science & IT
- The Cybersecurity Threat Landscape
- Cybersecurity Policy, Governance & Management
- Partner & Vendor Security Management
- Information Security Performance Metrics
- Information Security Compliance
- What is the ASCP Exam?
- ASCPI vs ASCP
- MEGA Exam Registration Information
- MEGA & MoGEA Prep Product Comparison
- PERT Prep Product Comparison
- MTLE Prep Product Comparison
- What is the MTLE Test?

- Gnosticism: Beliefs & Symbols
- Jagadish Chandra Bose: Biography, Inventions & Contributions
- White Whale in Moby-Dick: Symbolism, Meaning & Metaphor
- Impact of Competition on the Quality, Quantity & Price of Goods
- Whole Systems: Definition, Organizational Structures & Examples
- The Canterbury Tales: Gender Roles & The Role of Women
- Product Cloud & the Internet of Things: Definition & Example
- Quiz & Worksheet - What is an Algorithm?
- Writing a Topic Sentence: Quiz & Worksheet for Kids
- Quiz & Worksheet - Juror 2 in 12 Angry Men
- Quiz & Worksheet - What is Absolute Humidity?
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies
- Bullying in Schools
- Lesson Plans for Teachers

- ACT Math Prep: Review & Practice
- MTTC Psychology (011): Practice & Study Guide
- Physical Science Textbook
- NYSTCE Business and Marketing (063): Practice and Study Guide
- Intro to Music for Teachers: Professional Development
- The Historical Background of Astronomy
- Introduction to Literary Criticism: Homework Help
- Quiz & Worksheet - Board of Education of the Hendrick Hudson Central School District v. Rowley
- Quiz & Worksheet - Features of Health Education
- Quiz & Worksheet - Frostbite & Hypothermia First Aid
- Quiz & Worksheet - Conflicts in Julius Caesar
- Quiz & Worksheet - Charles by Shirley Jackson

- Decius Brutus in Julius Caesar
- Piet Mondrian: Biography, Paintings & Art
- Common Core Standards in Rhode Island (RI)
- How to See If Your School Accepts Study.com Credit
- Aerospace Engineering Scholarships for High School
- High School Summer Reading List
- How Long Does it Take to Learn a Language?
- How to Learn French
- Illinois Common Core Science Standards
- ELM Test Registration Information
- How to Learn French
- Jobs for Teachers Outside of Education

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject