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Congruence and Rigid Motion

Some transformations can be used to move geometric objects from one location to some other location. These transformations include reflections, rotations, and translations. All of these transformations will be studied in this chapter.
To translate a figure means to move it from one position to another position in a coordinate plane. The translation can be vertical, horizontal, or a combination of the two. A reflection of a figure means that each point of the figure is mirrored in a line. When a figure is rotated it means that it is turned around a point. This point is called the center of rotation.
These transformations are also referred to as rigid motions. In a transformation that is a rigid motion, distances between the points of the preimage are preserved.
In the final section of this chapter, we will discuss the concept of congruence. Congruence can be described as figures that can be mapped onto each other with rigid motions. When a geometric object is subjected to one or more rigid motions, the image and the preimage are congruent.
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