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# Math 8.1-8.7

### Chapter 8.1-8.7 (whole chapter) vocab

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

ratio of a to b | the quotient a/b if a and b are two quantities that are measured in the same units. can also be written a : b |

proportion | an equation that equates two ratios. a and d are called exetremes. c and b are called means. |

Cross Product Property | the product of the exetremes equals the product of the means.if a/b=c/d then ad=bc |

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

geometric mean | for two positive numbers a and b, the positive number x such that:a/x=x/b or x = the radical of axb |

similar polygons | two polygons such that their correspdoning angles are congruent and the lengths of the corresponding sides are proportional. |

scale factor | the ratio of the lengths of two corresponding sides of two similar polygons |

If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths | |

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 lengths of the corresponding sides of two triangles are proportional then the triangles are similar |

side-angle-side 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 the 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 |

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

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

Dilation | a type of transformation with center C and scale factor k that maps every point P in the plane to a point P' so the following properties are true:1. If P is not the center point C then the image point P' lies on ray CP. the scale factor k is a positive |

number such that k=CP'/CP and k is not equal to 12. If P is the center point C then P = P' | |

Enlargement | k is between 0 and 1 |

reduction | k is larger than 1 |

Created by:
jumpthemoon