Abstract
A primary concept of Motion Geometry is congruence. When the tracing of a figure can be superimposed on another in such a way that they just match,” the figures are congruent. There are three physical motions that, alone or in combination, leave a figure unchanged except for its position. These motions are slides, turns, and flips. By tracing a figure and then moving the tracing paper by sliding it, turning it, or flipping it, students learn to find the image of an original figure under one or more of these motions. A flip is a turnover motion about a line that serves somewhat the same purpose as a mirror. If there is a congruence of any type that maps a figure onto itself, the figure is said to be invariant under that congruence. Invariant means simply that a tracing of a figure may be matched with the figure itself in some nontrivial way.
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