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# WHS Ch 7 Similarity

### WHS Chapter 7 Similarity

Term | Definition |
---|---|

side of a polygon | one of the segments that form a polygon |

denominator | the bottom number of a fraction, which tells how many equal parts are in the whole |

numerator | the top number of a fraction, which tells how many parts of a whole are being considered |

vertex of a polygon | the intersection of two sides of a polygon |

vertical angles | two nonadjacent angles formed by two intersecting lines |

dilation | a transformation I which the lines connecting every point P with its preimage P' all intersect at a point C known as the center of dilation; a transformation that changes the size of a figure but not the shape |

scale | ratio between two corresponding measurements |

scale drawing | drawing that uses a scale to represent an object as smaller or larger than the actual object |

scale factor | multiplier used on each dimension to change one figure into a similar figure |

similar | two figures have the same shape but not necessarily the same size |

similar polygons | two polygons whose corresponding angles are congruent and whose corresponding side lengths are proportional |

similarity ratio | ratio of two corresponding linear measurements in a pair of similar figures |

similarity transformation | a dilation or a composite of one or more dilations and one or more congruence transformations |

reduction | the scale factor k in a dilation is a value between 0 and 1 |

AA Similarity Postulate | If two angles of one triangle are congruent to two angels of another triangle, then the triangles are similar |

SSS Similarity Theorem | If the three sides of one triangle are proportional to the three corresponding sides of another triangle, then the triangles are similar. |

SAS Similarity Theorem | If two sides of one triangle are proportional to two sides of another triangle and their included angels are congruent, then the triangles are similar |

Reflexive Property of Similarity | ∆ ABC ~ ∆ ABC |

Symmetric Property of Similarity | If ∆ ABC ~ ∆ DEF, then ∆ DEF ~ ∆ ABC. |

Transitive Property of Similarity | If ∆ ABC ~ ∆ DEF and ∆ DEF ~ ∆ XYZ, then ∆ ABC ~ ∆ XYZ. |

Triangle Proportionality Theorem | If a line parallel to a side of a triangle intersects the other two sides, then it divides those sides proportionally. |

indirect measurement | any method that uses formulas, similar figures, and/or proportions to measure an object |

If the similarity ratio of two similar figures is a:b , then the ratio of their perimeters is a:b , and the ratio of their areas is a²:b² or (a:b)². |