Back To Course

High School Geometry: Tutoring Solution14 chapters | 161 lessons

Watch short & fun videos
**
Start Your Free Trial Today
**

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 70,000 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:
*Karin Gonzalez*

Karin has taught middle and high school Health and has a master's degree in social work.

In this lesson, you will learn the definition of same-side interior angles, their properties when they lie on parallel lines, and the same-side interior angle theorem. At the end, you can test your knowledge with a quiz.

**Same-side interior angles** are a pair of angles on one side of a transversal line, and on the inside of the two lines being intersected. What is a transversal line, you may wonder? A **transversal line** is simply a line that intersects other lines. This may sound confusing, but this diagram should clear up any uncertainties.

Angles 3 and 6, indicated in pink, are same-side interior angles. Angles 4 and 5, indicated in green, are also same-side interior angles. And line *t* is the transversal line intersecting lines *a* and *b.*

If you look at the diagram, you might notice something else interesting. Lines *a* and *b* are parallel to each other! What are **parallel lines**? They are lines that run alongside each other that never intersect.

When transversal line *t* intersects parallel lines *a* and *b*, it makes the same-side interior angles 3 and 6 supplementary. Same-side interior angles 4 and 5 are also supplementary. **Supplementary angles** are angles that add up to 180 degrees.

Surprisingly, we have just covered the same-side interior angle theorem without even knowing it! The **same-side interior angle theorem** states that when two lines that are parallel are intersected by a transversal line, the same-side interior angles that are formed are supplementary, or add up to 180 degrees.

Let us look at two examples before ending this lesson. We will use to the same diagram in both examples.

**Example 1**

Let's pretend that we don't know if lines *a* and *b* are parallel. Let's pretend that we know that angle 4 is 100 degrees and angle 5 is 80 degrees. What conclusion can we draw about lines *a* and *b* now? That they are parallel! How do we know this? Because we know that same-side interior angles 4 and 5 equal 180 degrees. Therefore, we can draw the conclusion that lines *a* and *b* are parallel!

**Example 2**

Now, let's pretend that we know that lines *a* and *b* are parallel and angle 3 is 70 degrees. What conclusion could we draw about angle 6 knowing this information? We could conclude that angle 6 is 110 degrees! How can we do this? Because we know that lines *a* and *b* are parallel. Therefore, we know that the same-side interior angles 3 and 6 are supplementary, or that they add up to 180 degrees. Therefore, if angle 3 is 70 degrees, it would make its same-side interior angle, 6, 110 degrees!

**Same-side interior angles** are formed when a **transversal line** intersects two or more lines. When the lines that the transversal intersects are **parallel**, you get same-side interior angles that are **supplementary**, or add up to 180 degrees. If you don't know if the lines in a diagram are parallel, but you know that the same-side interior angles add up to 180 degrees, it's safe to draw the conclusion that the lines cut by the transversal line are parallel and vice versa.

- Same-side interior angles are formed from two parallel lines crossed by a transversal.
- Same-side interior angles add up to 180 degrees.
- To prove two lines are parallel, add up the same-side interior angles, or vice-versa.

Progress through this lesson in order to:

- Identify same-side interior angles
- Use the same-side interior angle theorem to prove parallel lines

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

Create
your account

Already a member? Log In

BackDid you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 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
20 in chapter 4 of the course:

Back To Course

High School Geometry: Tutoring Solution14 chapters | 161 lessons

- Area of Triangles and Rectangles 5:43
- Perimeter of Triangles and Rectangles 8:54
- How to Identify Similar Triangles 7:23
- Angles and Triangles: Practice Problems 7:43
- Triangles: Definition and Properties 4:30
- Classifying Triangles by Angles and Sides 5:44
- Interior and Exterior Angles of Triangles: Definition & Examples 5:25
- Constructing the Median of a Triangle 4:47
- Median, Altitude, and Angle Bisectors of a Triangle 4:50
- Constructing Triangles: Types of Geometric Construction 5:59
- Properties of Concurrent Lines in a Triangle 6:17
- 30-60-90 Triangle: Theorem, Properties & Formula 5:46
- 45-45-90 Triangle: Theorem, Rules & Formula 4:31
- Complementary Angles: Definition, Theorem & Examples 4:24
- Consecutive Interior Angles: Definition & Theorem 3:42
- Exterior Angle Theorem: Definition & Formula 6:06
- Half Angle: Rule, Formula & Examples
- Perfect Parabola: Definition & Explanation
- Same-Side Exterior Angles: Definition & Theorem 2:44
- Same-Side Interior Angles: Definition & Theorem 3:17
- How to Find Amplitude of a Sine Function
- How to Find the Area of an Equilateral Triangle
- How to Find the Area of an Isosceles Triangle 6:03
- Go to Properties of Triangles: Tutoring Solution

- Influence & Persuasion for Front-Line Managers
- Purpose-Driven Business Leadership
- Lean-Agile Mindset for Leaders
- Reducing Stress for Supervisors
- Team Building Skills for Supervisors
- Designing Influential Messages in Business
- Aligning Jobs, Goals, Purpose & Agenda
- Continuous Lean Process Improvement
- Overcoming Obstacles to Influence & Persuasion in Business
- Techniques & Tools for Influence in Business
- CLEP Exam Question Formats
- CLEP Exam Costs & Registration Deadlines
- CLEP Exam List & Credits Offered
- How to Request a CLEP Transcript
- CLEP Exam Dates & Testing Center Locations
- CLEP Scoring System: Passing Scores & Raw vs. Scaled Score
- Continuing Education Opportunities for Molecular Biology Technologists

- Human Resources Management for Hospitality
- Willowbrook Hepatitis Experiments: Bioethics Case Study
- The Full Cycle of Event Planning in a Hotel
- The Electrical Stimulation Method: Theorists, Research & Applications
- Higher-order Determinants Lesson Plan
- Using Anecdotes to Persuade an Audience
- What Are Civil Disturbance Operations?
- Value Creation in Business: Definition & Example
- Quiz & Worksheet - Angles in Standard Position
- Quiz & Worksheet - Sustainable Tourism
- Quiz & Worksheet - Rhetorical Devices in In Cold Blood
- Quiz & Worksheet - Personalistic & Naturalistic Theory in Science
- Quiz & Worksheet - Synopsis of Wonder by R.J. Palacio
- Tourism Marketing Flashcards
- Tourism Economics Flashcards

- 7th Grade Language Arts: Lessons & Help
- Praxis Physical Education: Practice and Study Guide
- Smarter Balanced Assessments - ELA Grades 6-8: Test Prep & Practice
- Life Science Curriculum Resource & Lesson Plans
- Middle School Language Arts: Lessons & Help
- CSET English IV: Oral Communication Processes: Speaking and Listening
- Earthquakes: Homework Help
- Quiz & Worksheet - Two-Factor Theory of Emotions
- Quiz & Worksheet - Function & Role of Hormones
- Quiz & Worksheet - Post-War Soviet Union & Eastern Europe
- Quiz & Worksheet - Effort Justification Characteristics & Studies
- Quiz & Worksheet - Mutagens as a Cause of Mutation

- The Pacific Ocean Theater of WWII: Japan vs. The Allies
- What Is JCAHO? - Definition, Accreditation Standards & Requirements
- 4th Grade Massachusetts Science Standards
- What Is the STAR Math Assessment?
- WV Next Generation Standards for Math
- How to Create a Classroom on Study.com
- Cool Math Puzzles
- Nevada State Science Standards
- Study.com's Guidance and Coaching Service
- How to Learn Spanish Fast
- What is CDT Certification?
- Georgia Physical Science Standards

Browse by subject