A double reflection in two parallel lines is the same as a translation.

 

Move the solid vertices on the blue polygon, and see how the other polygons respond..

We have shown that:

  • Successive reflections in two non-parallel lines produce a rotation;
  • Successive reflections in two paralllel lines produce a translation.

The converse is also true, namely:

  • Any rotation can be produced by a pair of reflections using non-parallel lines;
  • Any translation can be produced by successive reflections in parallel lines.

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