TenMarks teaches you how to identify rotational symmetry.
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In this lesson, let’s learn about rotational symmetry. Rotational symmetry is essentially when we take a figure and we rotate. Now, any figure, let’s take a square, if I rotate it by 360 degrees, that means it comes back to its original spot which means it will look exactly the same. So every figure can be rotated by 360 degrees. But for a figure to have rotationally symmetry, we should be able to rotate it by less than 360 degrees at least once. So, let’s try some examples. We’ll try example A, it looks like an X with the top and bottom covered with two triangles stuck on top of each other. So if we rotate it by 90 degrees, the figure shifts changes the shape. We rotated by another 90 degrees from the total rotation 180, this figure and this figure looks exactly the same. As I said, 0 to 360 will always look the same any. Because this at 180 degrees it looks the same, this figure does have rotational symmetry. What is the smallest faction we need? 180 degrees. 180 degrees gets us to rotationally symmetry. Let’s try another one. We’ll try three of these. If we have a square with the corners curved, at 90 degrees, 180, 270, 360, they all look the same. So this figure also has rotational symmetry and the smallest angle is 90 degrees. As long as they’re rotated by 190 degrees, it looks exactly like the first. 180 looks like the first as well. Let’s try the third example. When I take a smiley face and rotate it, well 90 degrees doesn’t work, 180 doesn’t work, 270 or 360, the only ones that work are 360. So this figure does not have rotationally symmetry. So what have we learned? Essentially, for a figure to have rotational symmetry, we should be able to rotate it by an angle less than 360 degrees. And when we do that, it should look exactly the same size, shape and place as the original figure.

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