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# Chapter 6 Notecards

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

Ratio of a to b | if a and b are two numbers or quantities and b does not = 0 then the ratio is a/b or a:b |

Proportion | an equation that states that two ratios are equal |

Means | The middles terms of a proportion |

Extremes of a Proportion | The first and last terms of a proportion |

Cross Products Property of Proportion | In a proportion the product of the extremes equals the product of he means. EX: If a/b = c/d and d does not = 0 then ad = bc |

Geometric Mean | two positive numbers a and b is the positive number x that satisfies a/x = x/b. so x^2 = ab and x = the square root of ab |

Additional Properties of Proportions | 2. Reciprocal Property: if two ratios are equal then their reciprocals are also equal. 3. If you interchange the means of proportion, then you from another true proportion. 4. In a proportion, if you add the value of each ratio's denominator to its nume |

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

Scale | a ratio that describes how the dimensions in the drawing are related to the actual dimensions of the object |

Similar Polygons | two polygons such that their corresponding angles are congruent & the lengths corresponding sides are proportional |

Scale Factor | the ratio of the length of two corresponding sides of two similar polygons |

Perimeters of Similar Polygons Theorem | if two polygons are similar then the ratio of their perimeters is equal to the ratios of their corresponding side lengths |

Corresponding Lengths in Similar Polygon | if two polygons are similar then the ratio of any two corresponding lengths in the polygons is equal to the scale factor of the similar polygons |

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

SSS Similarity Theorem | if the corresponding side lengths of two triangles are proportional, then the triangles are similar |

SAS Similarity Theorem | if an angle of one triangle is congruent to an 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 sides then it divides the two sides proportionally. |

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

Theorem 6.6 | if three parallel lines intersect two transversals, then they divide the transversals proportionally |

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

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