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# Geo ints unit 10

### unit 10 test theorems and postulates

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

concentric circles | sphere(s) whose centers are the same point |

minor arcs | measure of a minor arc equals the measure of the corresponding central angle |

Arc Addition Postulate | the measure of the arc formed by two adjacent arcs is the sum of the measure of the two arcs |

theorem 9-3 | in the same circle (or congruent circles) two minor arcs are congruent if and only if their central angles are congruent |

inscribed angle | an angle whose vertex is ON the circle and whose sides are chords of the circle |

theorem 9-7 | the measure of an inscribed angle is equal to half the measure of its intercepted arc |

corollary to the inscribed angle theorem | if two inscribed angles intercept the same arc (or congruent arcs) then the angles are congruent |

corollary 2 | an angle inscribed in a semicircle is a right angle |

corollary 3 | if a quadrilateral is inscribed in a circle, then its opposite angles are supplementary |

thm 9-1 and 9-2 | a line is tangent to a circle if and only if the line is perpendicular to a radius at the point of tangency |

corollary to thm 9-1 and 9-2 | tangents to a circle from (the same) point are congruent |

theorem 9-8 | the measure of an angle formed by a chord and a tangent is equal to half the measure of the intercepted arc |

theorem 9-9 | the measure of an angle formed by two chords that intersect inside a circle is equal to half the sum of the intercepted arcs |

theorem 9-10 (case 1) | two secants that meet outside of a circle from an angle is equal to half the difference of the arcs they intercept |

theorem 9-10 (case 2) | the angle formed by a tangent and a secant is half the difference of the intercepted arcs |

theorem 9-10 (case 3) | the angle formed by two tangents is half the difference of the intercepted arcs |

chord-chord power theorem ("power of E") | when two chords intersect inside a circle, the product of the segments of one chord equals the product of the segments of the other chord (pp x pp) |

secant-secant power theorem (power of "A") | when two secants are drawn to a circle from an external point, the product of one secant segment and its external segment equals the product of the other secant segment and its external segment (OW x OW) |

Secant-tangent power theorem (thm 9-13) | when a secant segment and a tangent segment are drawn to a circle from an external point, the product of the secant segment and its external segment is equal to the square of the tangent segment (OW x OW) |

Created by:
mtwhitneygirl