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# Geometry Chap. 9

### Vocabulary

Question | Answer |
---|---|

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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