# Math Theorems & Postulates

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## Triangles, Segments, and Properties

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

Segment Addition Postulate | If 3 points A B and C are collinear and B is between A and C, the AB + BC = AC |

Angle Addition Postulate | If point B is in the interior of angle AOC, then angle AOB + BOC = AOC and if AOC is a straight angle, then AOB + BOC = 180. |

Reflexive Property | If line AB is congruent to line AB then angle A is congruent to angle A |

Symmetric Property | If line AB is congruent to line CD then line CD is congruent to line AB |

Transitive Property | If line AB is congruent to CD and CD is congruent to EF then line AB is congruent to line EF |

Vertical Angles Theorem | Vertical angles are congruent. |

Congruent Supplements Theorem | If two angles are supplements of congruent angles, then two angles are congruent |

Congruent Complements Theorem | If two angles are complements of congruent angels, then the 2 angles are congruent |

Points of a Triangle

## Bisector Theorems

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

Triangle Midsegment Theorem | If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side and half its length |

Triangle Inequality Theorem | The sum of the lengths of any two sides of a triangle is greater than the length of the third side |

Perpendicular Bisector Theorem | If a point is on the perpendicular bisector of a segment, then it is equidistant from the enpoints of the segment |

Converse of Perpendicular Bisector Theorem | If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment |

Angle Bisector Theorem | If a point is on the angle bisector of an angle, then it is equidistant from the sides of the angle |

Converse of Angle Bisector Theorem | If a point is equidistant from the sides of an angle, then it is on the angle bisector. |

Hinge Theorm* | If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first triangle is greater than the included angle of the second triangle, then the third side of the first triangle is greater than the third side of the second triangle. |

## Circle Theorems

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

Equation of a Circle | The standard of an equation of a circle with center (h,k) and radius "r" is (x-h)2 + (y-k)2 = r2 |

Theorem 12-2 | If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency. |

Converse of Theorem 12-2 | If a line in the same plane as a circle is perpendicular to a radius at its endpoint on the circle, then the line is tangent to the circle. |

Theorem 12-4 | Two segments tangent to a circle from a point outside the circle are congruent. |

Theorem 12-5 | In the same circle or in congruent circles, (l) congruent central angles have congruent arcs, and (2) congruent arcs have congruent central angles |

Theorem 12-6 | In the same circle or in congruent circles, (1) congruent chords have congruent arcs, and (2) congruent arcs have congruent chords. |

Theorem 12-7 | A diameter that is perpendicular to a chord bisects the chord and its arc. |

Theorem 12-8 | The perpendicular bisector of a chord contains the center of the circle. |

Theorem 12-9 | In the same circle or in congruent circles, (1) chords equidistant from the center are congruent, and (2) congruent chords are equidistant from the center |

Inscribed Angle Theorem | The measure of an inscribed angle is half the measure of its intercepted arc |

Theorem 12-11 | The measure of an angle formed by a chord and a tangent that intersect on a circle is half the measure of the intercepted arc. |

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