2D Rotational Symmetry 

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Lesson Objective
This lesson shows you the ideas behind 2D Rotational Symmetry. Also, you will get to see a quick video demonstration on it.
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About This Lesson
When we rotate a shape about its center point, we may notice that at a certain angle, the rotated shape coincides with its 'not rotated' self (see picture). 

When this happens, the shape is said to has rotational symmetry. This lesson will show the ideas behind it. 

You can proceed by reading the study tips first or watch the math video or try out the practice questions.
rotational symmetry for a card

Study Tips

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Tip #1
When we rotate the triangle about its center point for 360o, we notice that it fits onto itself for 3 times for every 120o rotation.

By definition, the number of times a shape fits onto itself when rotated is called the order of symmetry.
Hence, we can see that the order of symmetry for this triangle is 3.

The math video below will show you more on this visually.
triangle rotational symmetry
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Tip #2
Now, this shape only fits onto itself 1 time after rotate for 360o. Hence, the order of symmetry is 1.

However, for any shape that has rotation symmetry of order 1, that shape is considered as not having any rotational symmetry.

Hence, this shape has no rotational symmetry.

no rotational symmetry
Now, watch the following math video to learn more.

Math Video

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Click play to watch video

If the above player doesn't work, try this direct link.

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Math Video Transcript

Practice Questions & More

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Multiple Choice Questions (MCQ)
Now, let's try some MCQ questions to understand this lesson better.

You can start by going through the series of questions on 2d rotational symmetry or pick your choice of question below.
  1. Question 1 on rotational and order of symmetry