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Can someone tell me what the thinking was behind not including glide reflection in the Common Core as one of the basic rigid symmetries of the plane, along with reflections, rotations, and translations? I know some people say glide reflections are more difficult to recognize, or that every glide reflection is a combinations of a translation and a reflection. However, every isometry may also be composed of a combination of reflections. Thanks!
In the Common Core rigid motions are used to define the idea of congruence, and to prove theorems about congruence, such as the criteria for congruence of triangles. This is different from the common use of transformations to study frieze patterns and tilings of the plane. Glide reflections figure prominently in the latter, but not so much in the former. Of course, this doesn’t forbid curriculum writers from naming and using glide reflections. But that is a a side trail from the main goal in the Common Core.
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