Back To Course

6th-8th Grade Math: Practice & Review55 chapters | 466 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

Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Jennifer Beddoe*

Symmetry occurs in many areas of mathematics. This lesson explains symmetry in math and explores the three basic types of symmetry: rotational symmetry, reflection symmetry, and point symmetry.

Symmetry comes from a Greek word meaning 'to measure together' and is widely used in the study of geometry. Mathematically, **symmetry** means that one shape becomes exactly like another when you move it in some way: turn, flip or slide. For two objects to be symmetrical, they must be the same size and shape, with one object having a different orientation from the first. There can also be symmetry in one object, such as a face. If you draw a line of symmetry down the center of your face, you can see that the left side is a mirror image of the right side. Not all objects have symmetry; if an object is not symmetrical, it is called **asymmetric**.

When working with symmetry, the initial image is called the **pre-image**, and the second image is called the **image** because it is the final step in the process. Just like the answer to a math problem is the final step in that process, the image is what is created when you rotate something 90 degrees or flip it about the *x*-axis. There are three basic types of symmetry: rotational symmetry, reflection symmetry, and point symmetry.

Sometimes called **line symmetry** or **mirror symmetry**, **reflection symmetry** is when an object is reflected across a line, like looking in a mirror. The face from before shows you reflection symmetry. Here are some more examples of reflection symmetry. The line of symmetry does not have to be vertical; it can go in any direction. Also, certain objects, like a square or a circle, can have many lines of symmetry.

Rotational symmetry occurs when an object is rotated about a fixed point. The object can be rotated more than once. The number of rotations is called the **order** of rotation. This image has been rotated three times and, therefore, has 'order four' (the pre-image is counted when determining the order of symmetry).

**Point symmetry** occurs when every part of an object has a matching part that is the same distance from the origin on a coordinate plane, but is in the opposite direction. Point symmetry is often called **origin symmetry** because the point is frequently the origin on the coordinate plane. Many playing cards have point symmetry - they look the same from top and bottom. Items with point symmetry look the same from other directions, too. If you were to cut a playing card in half at a 45 degree angle, the two sides would still look the same.

Objects are said to be symmetrical if their **pre-image** and **image** have the same size and shape, but are either mirror images of each other or one has been rotated to go in a different direction from the first. There are three basic types of symmetry: **reflection symmetry**, rotational symmetry, and **point symmetry**.

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 79 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
8 in chapter 42 of the course:

Back To Course

6th-8th Grade Math: Practice & Review55 chapters | 466 lessons

- What is a Line of Symmetry in Geometric Shapes? 3:19
- Congruence in Geometric Shapes 3:56
- Similarity in Geometric Shapes 6:03
- Parallel, Perpendicular and Transverse Lines 6:06
- Identifying Parallel Lines in Geometric Shapes 3:35
- Constructing Perpendicular Lines in Geometry 3:39
- Identifying Perpendicular Lines in Geometric Shapes 3:54
- What is Symmetry in Math? - Definition & Concept 2:54
- Go to 6th-8th Grade Geometry: Symmetry, Similarity & Congruence

- DSST Principles of Advanced English Composition: Study Guide & Test Prep
- Upper Level SSAT: Test Prep & Practice
- Sherlock Holmes: His Last Bow Study Guide
- The Return of Sherlock Holmes Study Guide
- The Adventures of Sherlock Holmes Study Guide
- Real World Shapes
- Data Distribution Overview
- Understanding Limits in Math
- Mathematical Process & Perspectives
- Understanding Vectors
- Registering for the TOEIC Listening & Reading Test
- TOEIC Listening & Reading Test: Purpose & Format
- Excelsior College BS in Business Degree Plan Using Study.com
- IELTS General Training Reading: Format & Task Types
- IELTS General Training Writing: Format & Task Types
- Gates-MacGinitie Reading Test Scores
- IELTS General Training Test: Structure & Scoring

- Spinous Process: Function & Fracture Treatment
- Research Based Learning Strategies
- Foreshadowing in Macbeth
- End-of-Period Worksheet: Definition & Example
- Botany Activities & Games
- Mexican Baroque Architecture: Characteristics & Examples
- Chester A. Arthur & The Civil War
- James Baldwin: Biography & Books
- Quiz & Worksheet - Short Story Elements
- Quiz & Worksheet - Slave Trade Compromise
- Quiz & Worksheet - Radicands
- Quiz & Worksheet - Characteristics of SEP IRAs
- Muscle Contraction Flashcards
- Water Polo Flashcards

- 12th Grade English Curriculum Resource & Lesson Plans
- SAT Math Prep: Review & Practice
- AP World History: Tutoring Solution
- Saxon Algebra 1 Homeschool: Online Textbook Help
- Algebra for Teachers: Professional Development
- Blood Disorders - Anemia: Help and Review
- Water Balance: Tutoring Solution
- Quiz & Worksheet - Turning Text into a Film or Live Production
- Quiz & Worksheet - Carrying Capacity, Migration & Dispersion
- Quiz & Worksheet - Ecosystems, Habitats and Ecological Niches
- Quiz & Worksheet - Luteal Phase of the Ovarian Cycle
- Quiz & Worksheet - PowerPoint Print Options

- Impact of Word Choice on Meaning and Tone
- Price Elasticity of Demand: Definition, Formula & Example
- 2nd Grade Word Walls
- Kindergarten Writing Prompts
- Reading Games for Kids
- Preschool Math Centers
- Social Studies Games for Kids
- 100th Day of School Project Ideas
- Finding Travel Grants for Teachers
- Writing Prompts for Middle School
- Fairfax County Adult Education
- Missouri Alternative Teacher Certification

Browse by subject