Common Core Standards: Math
High School: Geometry
3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
By this point, students should know that transformations are movements of geometric figures on the coordinate plane. Now, it's simply a matter of building on this concept. It's just an extension of the last two standards, so hopefully it'll be kind of a no-brainer.
Students should be able to work with some geometric shapes, including parallelograms, trapezoids, and more. They should not only describe, but also identify and use points of symmetry.
In plain English, students have to illustrate how a figure is mapped onto itself by simply using a transformation without changing the shape or size of the figure. To do that, they'll need to calculate how much symmetry exists between the images, both among their lines (through reflection) and degrees (through rotational movement).
One important thing to keep in mind, though: properties such as side lengths and angle measures of the objects are key. You only have to rotate a regular hexagon 60° for it to carry onto itself, but a square needs 90°.
Both the concepts of symmetry and "carrying a geometric shape or figure onto itself" can be found in things like wallpapers, clothing, computer screensavers, and much more. If you ever need examples for symmetry, nature's got your back. And if nature's raining on your parade, then computer-generated images get pretty close to the real deal nowadays.