Question Video: Identifying Symmetry in Three-Dimensional Figures | Nagwa Question Video: Identifying Symmetry in Three-Dimensional Figures | Nagwa

Question Video: Identifying Symmetry in Three-Dimensional Figures Mathematics

Consider the following solid. Does the solid have plane symmetry? Does the solid have an axis of symmetry?

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Video Transcript

Consider the following solid. Firstly, does the solid have plane symmetry? And secondly, does the solid have an axis of symmetry?

The shape in the diagram is a cylinder. A solid will have plane symmetry if we can cut the shape, in this case the cylinder, into two halves, where one is the mirror image of the other.

In terms of the cylinder, we could do this by cutting it horizontally, as shown in the diagram. Alternatively, we could cut the cylinder into two halves, where one is a mirror image of the other, vertically. As the cylinder can be cut into two halves, we can say yes, it does have plane symmetry.

A solid will have an axis of symmetry if, when rotated, it looks exactly the same. The cylinder has an axis of symmetry going down the middle, as when we rotate the cylinder, it will look identical at each point of the rotation. We can, therefore, say that it has an infinite order of rotational symmetry. In answer to the question, we can say yes, the solid does have an axis of symmetry. In summary, a cylinder has plane symmetry and also has an axis of symmetry.

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