12.2.1 Symmetry (continued)
Whether a figure has line symmetry is determined in this example. This figure has four lines of symmetry. Notice that the portions of the object on either side of each of the lines are reflections of each other. Or, if the object were reflected across one of the lines of symmetry, the image would lie exactly on top of the preimage.
Example 2 Identifying Rotational Symmetry
Whether a figure has rotational symmetry, the angle of any symmetry, and the order of symmetry are determined in this example. The triangle has rotational symmetry. Turning the triangle about its center will produce an image that coincides with the preimage. The angle of rotational symmetry is 120° and the order of the symmetry is 3. A turn of 120° degrees will form an image that coincides with the preimage. Three such turns return the original preimage. The arch does not have rotational symmetry. There is not a point around which the arch can be turned to produce an image that coincides with the preimage. The star has rotational symmetry. The angle of rotational symmetry is 72° and the order of the symmetry is 5.
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