This sketch is for a pretty open-ended investigation of motions, in the spirit of Euclid. There are many relationships in the sketch.[br][br]1) Make lists of which polygons are congruent to each other. How do you recognize them? No dragging yet. When your lists are complete, try dragging shapes. When you hit an original, it will move all of its images. Was your list correct?[br][br]Euclid thought of the motions as how you got from one shape to a congruent shape. Every pair of congruent shapes is linked by a single motion. So he decided that four motions were needed: the famous three being slide (translation), flip (reflection) and turn (rotation). The other, less popular, motion is a glide reflection.[br][br]2) Pick one of the congruent shape families. Identify the motion that moves each shape in the family to all of its congruent images. There should be 10 motions to figure out for each family.[br][br]3) Click the Show Lines button. For the same shapes as in (2), identify which shapes are reflections of each other across these lines.[br][br]4) Synthesis: how is it possible that shapes are moved with different motions to each other (as in 2) and are also all made by reflections of each other (as in 3)?

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