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# Geometry Chap. 9

### Vocabulary

Transformation A geometric figure is a function, or mapping that results in a change in the position, shape, or size of the figure.
Preimage The original image of a transformation.
Image The resulting image of a transformation.
Rigid Motion A transformation that preserves distance and angle measures.
Translation A transformation that maps all points of a figure the same distance in the same direction.
Composition of Transformations A combination of two or more transformations.
Reflection When you reflect a figure the shapes have opposite orientations.
Line of a Reflection A transformation with the following properties: if a point A is on line m, then the image of A is itself (that is, A' = A); if a point B is not on line m, the m is the perpendicular bisector of line BB'.
Rotation Preserve distance, angle measures, and orientation of figures.
Center of Rotation A transformation with these two properties: the image of Q is itself (that is, Q' = Q) and for any other point V, Qv' = QV and m<VQV' = x.
Angle of Rotation The number of degrees a figure rotates.
Symmetry A figure has symmetry if there is a rigid motion that maps the figure onto itself.
Line Symmetry/Reflectional Symmetry If there is a reflection for which the figure is its own image.
Line of Symmetry The line of reflection.
Rotational Symmetry If the image, after a rotation of less than 360 degrees, is exactly the same as the original figure.
Point Symmetry If a 180 degree rotation about a center of rotation maps the figure onto itself.
Glide Reflection The composition of a translation (a glide) and a reflection across a line parallel to the direction of a translation.
Isometry A transformation that preserves distance, or length.
Congruent Two figures are congruent if and only if there is a sequence of one or more rigid motions that maps one figure onto the other.
Congruent Transformation Also know as Isometry, is a transformation in which an original figure and its image are congruent.
Dilation A transformation (notation) that produces an image that is the same shape as the original, but is a different size. A dilation stretches or shrinks the original figure.
Center of Dilation A fixed point in the plane about which all points are expanded or contracted. The only invariant point under a dilation.
Scale Factor of a dilation The ratio of any two corresponding lengths in two similar geometric figures. Note: the ratio of areas of two similar figures is the square of the scale factor. The ratio of volumes of two similar figures is the cube.
Enlargement A dilation is an enlargement if the scale factor n is greater than 1.
Reduction The dilation is a reduction if the scale factor n is between 0 and 1.
Similarity Transformation A composition of a rigid motion and a dilation.
Similar Resembling without being identical.
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