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# Module 14 - 15

### This contains postulates and theorems of Module 14 - 15.1

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

Vertical Angles Theorem | If 2 angles are vertical angles, then the angles are congruent |

Transversal | a line that intersects at least 2 coplanar lines at 2 different points |

Corresponding angles | lie on the same side of the transversal and the same side of intersected lines |

Same-side interior angles | lie on the same side of the transversal and between the intersected lines |

Alternate interior angles | nonadjacent angles that lie on the opposite sides of the transversal between the intersected lines |

Alternate exterior angles | lie on the opposite sides of the transversal and outside the intersected lines |

Same-side interior angles postulate | If 2 parallel lines are cut by a transversal then the pairs of same-side interior angles are supplementary |

Alternate Interior Angles Theorem | If 2 parallel lines are cut by a transversal, then the pairs of alternate interior angles have the same measure |

Corresponding Angles Theorem | If 2 parallel lines are cut by a transversal, then the pairs of corresponding angles have the same measure |

Converse of the Same-Side Interior Angles Postulate | If 2 lines are cut by a transversal of same-side interior angles are supplementary, then the lines are parallel |

Converse of the Alternate Interior Angles Theorem | If 2 lines are cut by a transversal so that any pair of alternate interior angles are congruent, then the lines are parallel |

Converse of the Corresponding Angles Theorem | If 2 lines are cut by a transversal so that any pair of corresponding angles are congruent, then the lines are parallel |

The Parallel Postulate | Through a point P not on line l, there is exactly one line parallel to l |

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

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

Triangular Sum Theorem | the sum of the angle measures of a triangle is 180 degrees |

Polygon Angle Sum Theorem | the sum of the measures of the interior angles of a convex polygon with n sides is (n-2)(180 degrees) |

Exterior Angle Theorem | the measure of an exterior angle of a triangle is equal to the sum of the measures |

Regular Polygon | all sides are equal; all angles are equal |

Isosceles triangle | a triangle with at least two congruent sides |

Isosceles Triangle Theorem | If 2 sides of a triangle are congruent, then the two angles opposite the sides are congruent |

Equilateral Triangle Theorem | If a triangle is equilateral, then it is equiangular |

Converse of the Equilateral Triangle Theorem | If a triangle is equiangular, then it is equilateral |

Triangle Inequality Theorem | The sum of any two side lengths of a triangle is greater than the 3rd side length 1. AB + BC > AC 2. BC + AC > AB 3. AC + AB > BC |

Side-Angle Relationships in Triangles | If 2 sides of a triangle are not congruent, then the larger angle is opposite the longer side |

Angle-Side Relationships in Triangles | If 2 angles of a triangle are not congruent, then the longer side is opposite the larger side |

Circumcenter Theorem | The perpendicular bisectors of the side of a triangle intersect at a point that is equidistant from the vertices of the triangle |