Weight Loss Made a Bit Easier: Realistic and Practical Advice for Healthy Eating and Exercise
Available on Amazon.com in paperback/Kindle formats for $6.25/$2.99. Please click here for details.
Home | My Math and Education Books | Math Lessons | Ask a Math Question
Site Info | Contact Info | Tutoring Info | LarryZafran.com | Tweet
Lesson 29: Introduction to Symmetry
Symmetry is a favorite topic among test-makers, and it's an easy topic once you understand what the word means. It's also a word that comes up somewhat often in everyday life, especially in matters involving art, photography, and design.
Don't forget to watch the embedded video clip for this lesson at the bottom of the page. Please be sure to read the embedded video information and disclaimer.
The definition of symmetry needs to be memorized. If a shape has a line of symmetry, it means that each side of the line is a "mirror image" of the other. Think about a butterfly. If you draw an imaginary line down the center, and each side will be a mirror image of the other. We can say that the butterfly is symmetric or symmetrical, and that it has a vertical line of symmetry, since we need to draw an "up-down" line to show that the left half is the mirror image of the right half.
Some shapes have both a vertical as well as a horizontal line of symmetry. Think about a rectangle. If you draw a horizontal (left to right) line across the middle of a rectangle, the top half will be the mirror image of the bottom half. We could also draw a vertical (up-down) line, and we'd see that the left half of the rectangle would be the same as the right half. We can say that the rectangle has two lines of symmetry.
One way to help determine if a shape has a line of symmetry is to draw what you think is a line of symmetry, and then fold the shape along that line. The two sides should be exact mirror images of each other. If you do this with a symmetrical shape drawn on thin paper, you might be able to see that when one side is folded directly on top of the other, they will line up perfectly.
Sometimes a test question will show you some capital letters of the alphabet, and ask you to determine which ones have one line of symmetry, and which ones have two. Certainly many letters have none. Take a look at these capital letters, and try to see where the lines of symmetry are. For practice, try it yourself on paper.
- Zero Lines of Symmetry: F, G, J, L, N, P, Q, R, S, Z
- One Line of Symmetry: A, B, C, D, E, K, M, T, U, V, W, Y
- Two Lines of Symmetry: H, I, O, X
Some objects have what is called point symmetry. What this means is that if you rotate the object 180° (a half-circle) around a point, it will look the same. Stated another way, it looks the same upside-down. A good example is the letter S and the letter Z. See if you can think of some other examples.
Remember that you can
ask a math question if you have additional
questions about a topic, or you can
contact me if you have any comments
or suggestions for this site.