Tell whether each figure has rotational symmetry. If so, give the angle of rotational symmetry a

Tell whether each figure has rotational symmetry. If so,...

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Key Concepts

Angle of Rotational Symmetry

The angle of rotational symmetry is the smallest angle through which a shape can be rotated about its center and still appear unchanged. It is an important measure in identifying how the symmetry of a figure is quantified and determines the degree of rotation needed for the shape to match its initial configuration.

Rotational Symmetry

Rotational symmetry refers to a characteristic of a shape in which the shape can be rotated (less than a full circle) about a central point and still look the same as the original figure. This concept is fundamental to the study of geometric transformations and helps in understanding how figures behave under rotations.

Order of Symmetry

The order of symmetry of a figure is the number of times the figure maps onto itself as it is rotated through 360 degrees. This concept not only indicates how many rotational invariances a shape has but also plays a significant role in classifying geometric figures based on their symmetry properties.

Transcript

00:02 Hello there.

00:03 This question asks us to tell whether a figure has rotational symmetry, and if it does give the angle of the rotational symmetry and the order of the symmetry.

00:14 So just to start with the definition, remember that rotational symmetry means that an object can be rotated about a point, and you're looking for more than zero degrees and less than 360 degrees, so that the image go in size of the pre -image.

00:28 So all that means in layman's terms is that we can rotate an image and it still looks the same at some point while we're rotating.

00:36 So we're given a hexagon in this case and i've drawn a hexagon might be imperfect, but it's a hexagon.

00:45 And i made the top red just so we could track what's going on as we rotate this image.

00:50 So i'm going to grab my copy of the hexagon here and i'm going to put the two on top of each other.

00:56 So there's the image coinciding with the pre -image.

00:58 That is an exact copy.

01:00 And now let's rotate the copy and see what happens.

01:04 We rotate.

01:05 You can see right here, if i had drawn a perfect hexagon, that would line up.

01:11 And then you can just kind of work with me and imagine this a little bit.

01:14 Rotate again, and it matches again when the sides line up here.

01:21 Rotate again...

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