2D Rotational Symmetry

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Lesson Objective

This lesson shows you the ideas behind 2D rotational symmetry and 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 have rotational symmetry. This lesson will show you the ideas behind it.

You can proceed by reading the study tips first or watch the math video. You can try out the practice questions after that.

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 will 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 will only fits onto itself for 1 time after it is been rotated 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

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Math Video Transcript

This is a quick demonstration on two-dimensional rotational symmetry.

Now, let's consider this card. when I rotate this card about this point, for 360 degrees, observe how many times this card fits onto itself.

Let's start. One. Two.

So, we can see that, the card fits onto itself for 2 times.

Hence, with this observation, we can say that this card has rotation symmetry of order, 2.

Alright, let's take another example. Consider this flower.

When I rotate this flower about this point, for 360 degrees, observe how many times this flower fits onto itself.

Let's start. one. two. three. four. five.

So, we can see that, the card fits onto itself for 5 times.

Hence, we can say that this flower has rotation symmetry of order, 5.

That is all for this lesson. Try out the practice question to further your understanding.

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.

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