Back To Course

Geometry: High School15 chapters | 160 lessons

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 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:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Polygons are everywhere! In this lesson, you will learn what they are and what they look like. You will also learn about a special class of polygons and how to find its angles.

A **polygon** is any 2-dimensional shape formed with straight lines. Triangles, quadrilaterals, pentagons, and hexagons are all examples of polygons. The name tells you how many sides the shape has. For example, a triangle has three sides, and a quadrilateral has four sides. So, any shape that can be drawn by connecting three straight lines is called a triangle, and any shape that can be drawn by connecting four straight lines is called a quadrilateral.

All of these shapes are polygons. Notice how all the shapes are drawn with only straight lines? This is what makes a polygon. If the shape had curves or didn't fully connect, then it can't be called a polygon. The orange shape is still a polygon even if it looks like it has an arrow. All the sides are straight, and they all connect. The orange shape has 11 sides.

I've mentioned a few polygons and have shown you a few common shapes. Here is a list of those in addition to several more:

Shape | # of Sides |
---|---|

Triangle | 3 |

Square | 4 |

Rectangle | 4 |

Quadrilateral | 4 |

Pentagon | 5 |

Hexagon | 6 |

Heptagon | 7 |

Octagon | 8 |

Nonagon | 9 |

Decagon | 10 |

n-gon |
n sides |

The last entry includes the general term for a polygon with *n* number of sides. Polygons aren't limited to the common ones we know but can get pretty complex and have as many sides as are needed. They can have 4 sides, 44 sides, or even 444 sides. The names would be 4-gon, or quadrilateral, 44-gon, and 444-gon, respectively. An 11-sided shape can be called an 11-gon.

A special class of polygon exists; it happens for polygons whose sides are all the same length and whose angles are all the same. When this happens, the polygons are called **regular polygons**. A stop sign is an example of a regular polygon with eight sides. All the sides are the same and no matter how you lay it down, it will look the same. You wouldn't be able to tell which way was up because all the sides are the same and all the angles are the same.

When a triangle has all the sides and angles the same, we know it as an equilateral triangle, or a regular triangle. A quadrilateral with all sides and angles the same is known as a square, or regular quadrilateral. A pentagon with all sides and angles the same is called a regular pentagon. An *n*-gon with sides and angles the same is called a regular *n*-gon.

Here is a regular triangle, a regular quadrilateral, and a regular pentagon. Do you see how all the sides are the same and no matter how you flip it, it will look the same?

Regular polygons also have two different angles related to them. The first is called the **exterior angle**, and it is the measurement between the shape and each line segment when you stretch it out past the shape.

However many sides a polygon has is the same number of exterior angles it has. So, a pentagon with five sides has five exterior angles. A hexagon will have six exterior angles and so on. For regular polygons, we can figure out the measurement of the exterior angle, but for polygons that aren't regular, we can't. Here is the formula for regular polygons:

The *n* stands for the number of sides the polygon has. So, a pentagon has exterior angles that measure 360 / 5 = 72 degrees.

The second angle is called the **interior angle**, which is the supplementary angle to the exterior angle. This means that the interior angle together with the exterior angle will add up to 180 degrees.

You can also say that the interior angle is the measurement of each corner of the polygon. Here is the formula for the interior angle:

The second formula is the same as the first, just rearranged. Don't worry about how we got there right now; just remember one or the other, and you will be okay. The second one is the more commonly seen in the math world. Let's look at an example. For our pentagon with five sides, using the first equation gives us 180 - 360 / 5 = 180 - 72 = 108 degrees. Using the second equation, we get (5 - 2) * 180 / 5 = 3 * 180 / 5 = 540 / 5 = 108 degrees. Both formulas will give us the same answer. Choose the formula that is easier for you to remember.

Polygons are all around us. Who of us has ever seen a triangle or a square? A **polygon** is defined as a 2-dimensional shape with straight sides. **Regular polygons** have sides and angles that are all the same. While you can find the measurements of the exterior and interior angles of regular polygons, you can't with polygons that aren't regular.

After this lesson, you should be able to:

- Define polygon and regular polygon
- Identify examples of polygons and regular polygons
- Explain how to find the exterior and interior angles of regular polygons

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
13 in chapter 7 of the course:

Back To Course

Geometry: High School15 chapters | 160 lessons

- Ratios and Proportions: Definition and Examples 5:17
- Geometric Mean: Definition and Formula 5:15
- Angle Bisector Theorem: Definition and Example 4:58
- Solving Problems Involving Proportions: Definition and Examples 5:22
- Similar Polygons: Definition and Examples 8:00
- The Transitive Property of Similar Triangles 4:50
- Triangle Proportionality Theorem 4:53
- Constructing Similar Polygons 4:59
- Properties of Right Triangles: Theorems & Proofs 5:58
- The Pythagorean Theorem: Practice and Application 7:33
- The Pythagorean Theorem: Converse and Special Cases 5:02
- Similar Triangles & the AA Criterion 5:07
- What is a Polygon? - Definition, Shapes & Angles 6:08
- Go to High School Geometry: Similar Polygons

- Chemistry 304: Organic Chemistry II
- ILTS Information Guide
- Introduction to Cloud Computing
- Praxis Elementary Education - Content Knowledge (5018): Study Guide & Test Prep
- CTEL Information Guide
- Atomic Structure in Chemistry Basics
- Equilibrium in Chemistry Basics
- Weathering, Erosion & Wasting Basics
- Overview of Waves, Sound & Light
- Overview of Types of Reactions in Chemistry
- Texas Teacher Certification Test Limit Waiver
- AFOQT Cost
- What Does the HESI A2 Nursing Exam Consist of?
- How to Learn Pharmacology for NCLEX
- What Are Considered Higher-Level Questions on the NCLEX?
- How to Study for NCLEx in 2 Weeks
- How Hard Is the ASVAB

- The Teacher's Role in Socializing Students to Be Physically Active
- Addressing Different Learning Styles in PE Programs
- Cardiorespiratory Fitness Activities for Various Levels
- First Language vs. Second Language Acquisition
- Regular Expressions in SQL Server Databases: Implementation & Use
- IPv6 Address: Impact, Structure & Types
- Real-World Implementations of Cloud Computing
- Network Switching: Definition & Types
- Quiz & Worksheet - Space Awareness & Body Movement
- Quiz & Worksheet - Boy by Roald Dahl
- Quiz & Worksheet - Sexual Frustration
- Quiz & Worksheet - Teenage Heart Attack Symptoms
- Quiz & Worksheet - Aerobic Endurance
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies

- PSAT Prep: Practice & Study Guide
- Fundamental Geometry
- Middle School Physical Science: Tutoring Solution
- DSST Criminal Justice: Study Guide & Test Prep
- Introduction to Psychology: Certificate Program
- WEST Middle Grades Math: Exponents & Exponential Expressions
- WEST Middle Grades Math: Factoring
- Quiz & Worksheet - Veterinary Wellness Programs
- Quiz & Worksheet - Production in Different Economic Systems
- Quiz & Worksheet - Africa's Hunter-Gatherer & Stateless Societies
- Quiz & Worksheet - The Fall of the Qing Dynasty
- Quiz & Worksheet - Factor Trees

- Genomes: Gene Number, Density & Size
- Hamlet Act 4, Scene 6 Summary & Quotes
- Place Value Games for Kids
- Special Education Laws in Florida
- Texas Teacher Certification Renewal
- ESL Teacher Organizations
- South Dakota Science Standards for Kindergarten
- Missouri Alternative Teacher Certification
- Illinois Common Core Science Standards
- First Grade Classroom Management Plan
- Illinois Science Standards
- South Dakota Science Standards for Kindergarten

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

Browse by subject