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# Math: Chapter 6

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

Ratio | a/b a:b a to b |

Proportion | An equation that states two ratios are equal. a/b=c/d |

Mean | In a/b=c/d b and c are the means. |

Extreme | In a/b=c/d a and d are the extremes. |

Geometric Mean | The positive number that satisfies a/x=x/b so x |

Ratio | a/b a:b a to b |

Proportion | A equation that states tow ratios are equal. a/b=c/d |

Extreme | In a/b=c/d A and D are the extremes. |

Mean | In a/b=c/d B and C are the means. |

Geometric Means | The positive number x that satisfies a/x=x/b so x•x=ab and x=√ab. |

Cross Product Property | The Product of the extremes equals the products of the means. ad=bc |

Scale Drawing | A drawing that is the same shape as the object it represents. |

Scale | The ratio that describes how the dimensions in a scale drawing are related to the original dimensions of the real object. |

Reciprocal Property | If two ratios are equal their reciprocals are also equal. a/b=c/d then b/a=d/c |

Means Property | If you interchange the means of a proportion then you form another true proportion. |

Denominator Property | If you add the value of each ratios denominator to its numerator, then you form another true proportion. |

SImilar Polygons | If corresponding sides are proportional and corresponding angles are congruent then figures are similar. Represented by ~ |

Scale Factor | The ratio of two corresponding lengths of two similar polygons. |

Perimeters of Similar Polygons Theorem | If two polygons are similar the ratios of the perimeters is equal to the scale factor. |

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

Side Side Side Similarity Theorem | If the corresponding side lengths of two triangle are proportional then the triangles are similar. |

Side Angle SIde Similarity Theorem | If an angle of one triangle is congruent to the corresponding angle of a second triangle and the lengths of the sides including these angles are proportional then the triangles are similar. |

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

Converse of the Triangle Proportionality Theorem | If a line divides two side of a triangle proportionally then it is parallel to the third side. |

Theorem 6.6 I | If three parallel intersect two transversals then they divide the transversals proportionally. |

Theorem 6.7 | If a ray bisects an angle of a triangle then it divides the opposite side into segments that are proportional to the length of the other two sides. |

Dialation | A transformation that stretches or shrinks a figure to create a similar figure. |

Reduction | If the scale factor of a dilation is greater than zero but less than one the dilation is a reduction. |

Enlargement | If the scale factor of a dilation is greater than one it is an enlargement. |