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

- PECT PreK-4: Practice & Study Guide
- ISEE Middle Level: Practice & Study Guide
- ISEE Lower Level: Practice & Study Guide
- ISEE Upper Level: Practice & Study Guide
- California Red Cross Nurse Assistant Competency Evaluation (CNA Test) Training
- Studying for Math 105
- Assessment in Early Childhood Education
- Instructional Strategies for Learners with Special Needs
- Teaching Health to Young Learners
- Academic Language & Sentence Structure for Young Learners
- What Are WIDA Standards?
- WIDA Can Do Descriptors for Kindergarten
- Demographics for English Language Learners
- Is the TAP Test Hard?
- What is Professional Development for Teachers?
- MTEL Content Test Requirements
- How to Earn Kanban Certification

- Market Research: Definition, Analysis & Methodology
- SCM Case Study: Decision Making at 3M
- Primase: Definition & Function
- Individual & Team Dynamics in the Hospitality Industry
- Relationships of Quantities with Whole Numbers: Lesson for Kids
- Artturi Virtanen: Biography & Contribution
- The Anaconda Plan in the Civil War Lesson for Kids
- Urosepsis: Definition, Symptoms, Complications & Treatment
- Quiz & Worksheet - Female Reproductive Diseases & Disorders
- Quiz & Worksheet - How to Price a Bond
- Quiz & Worksheet - Calculating Margin of Safety in Accounting
- Quiz & Worksheet - Effective Teaching with DAPs
- Graphing & Evaluating Equations & Functions Flashcards
- Exponential & Logarithmic Function Flashcards

- Things Fall Apart Study Guide
- Anthropology Textbook
- ScienceFusion Matter and Energy: Online Textbook Help
- Business 308: Globalization & International Management
- NMTA School Counselor: Practice & Study Guide
- HiSET: Earth's Spheres & Internal Structure
- 5th Grade Math: Estimation & Rounding
- Quiz & Worksheet - Diffraction & Huygen's Principle
- Quiz & Worksheet - Parabolic Path
- Quiz & Worksheet - Transport Layer of the OSI Model
- Quiz & Worksheet - Elasticity of Demand Formula
- Quiz & Worksheet - Cations

- Longitude: Definition & Examples
- The Long March: Definition & Reason
- Math Project Rubrics
- How to Earn Kanban Certification
- Online Credit Recovery Programs
- NCLEX Registration
- Reading Comprehension Activities
- NCLEX Pass Rates
- Resources for Teachers of English Language Learners
- How to Pass the HESI Entrance Exam
- How to Learn Java
- Pre-K Word Walls

Browse by subject