Line and Rotational Symmetries of 2-D Shapes

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  • 0:01 What is Symmetry?
  • 0:42 Line Symmetry
  • 1:13 Examples of Line Symmetry
  • 1:46 Rotational Symmetry
  • 2:55 Examples of Rotational…
  • 3:45 Lesson Summary
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Lesson Transcript
Instructor: Kevin Newton

Kevin has edited encyclopedias, taught middle and high school history, and has a master's degree in Islamic law.

One of the most important concepts in geometry is the idea of symmetry. But what does it actually mean? This lesson explains the difference between line symmetry and rotational symmetry.

What is Symmetry?

Have you ever looked at yourself in the mirror? Unless you are a vampire, chances are you see yourself in the reflection. Move your hand to your face, and the image in the mirror does the same. Make a funny face, and you get one back at you. What you are seeing in the mirror is a symmetry of you. Symmetry is the word used to define when the exact same thing occurs on the other side of a point of reference. By point of reference, I just mean something in between you and the reflection. In this lesson, we will look at the two most common types of symmetry: line symmetry and rotational symmetry.

Line Symmetry

When you look in the mirror, you are getting a mirror image of yourself. Mathematicians have a name for this type of symmetry. They call it line symmetry. Line symmetry gets its name because the symmetry takes place across a line. It is not just some ultra tiny point of you that is reflected, but all of you, and everything within range of the mirror. Everything is reflected by the whole length of the line of that mirror. In fact, some people even refer to this type of symmetry as mirror symmetry.

Examples of Line Symmetry

A mirror is a great example of an image of line symmetry, but it is far from the only one. Try this for example. Draw a smiley face. Nothing too detailed, in fact, the more basic the better. Now draw a vertical line right through the middle of it. Could you fold the paper in half and have the drawing of the smiley face meet up with other parts of the drawing perfectly across from it? Chances are you can. This is also an example of line symmetry.

Rotational Symmetry

There is another very basic type of symmetry worth mentioning, called rotational symmetry. Rotational symmetry happens when you can spin an image around a point, and it retains symmetry. This is different from the line symmetry we discussed earlier, as that symmetry did not involve moving the image. Rotational symmetry, on the other hand, requires it.

Rotational symmetry comes in different varieties, and to understand those, we'll need the help of a propeller and a star. Imagine a propeller with two blades attached to an airplane. Now in your mind, spin that propeller around. Does it ever match up exactly with where it had been before without rotating all the way around? Yes, once you rotate it halfway around the point, you'll see it matches up perfectly. We refer to this as an order 2 rotational symmetry, because it is symmetrical twice within one turn. Likewise, if you added a third blade to that propeller, assuming all were spaced evenly from each other, it would have order 3 symmetry.

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