Postulates and also theorems relating to parallel lines and also transversals -- straight from the text. Great for practicing complete and accurate wording so you will use them properly in future proofs. -- Theorem numbers are provided only for reference to the textbook. The important parts come study space the words of the theorems themselves, together with their meanings.

You are watching: In a plane, if two lines are perpendicular to the same line, then they are

AB | |

If 2 parallel lines are cut by a transversal, then each pair of matching angles is congruent. | |

Theorem 3-1 alternating Interior | If two parallel lines are cut by a transversal, then each pair of alternating interior angle is congruent, |

Theorem 3-2 Consecutive internal Angles | If 2 parallel lines are reduced by a transversal, then each pair the consecutive interior angles is supplementary |

Theorem 3-3 alternative Exterior Angle | If 2 parallel currently are cut by a transversal, climate each pair of alternative exterior angle is congruent, |

Theorem 3-4 Perpendicular Transversal | In a plane, if a heat is perpendicular to one of two parallel lines, then it is perpendicular come the other. |

Postulate 3-5 Parallel Postulate | If over there is a line and a allude not ~ above the line, climate there exists precisely one heat though the suggest that is parallel to the given line. |

Postulate 3-4 matching Angles (converse) | If two lines in a aircraft are reduced by a transversal therefore that corresponding angles space congruent, then the lines space parallel. |

Theorem 3-5 Alt Ext angles (converse) | If 2 lines in a airplane are reduced by a transversal so the a pair of alternating exterior angles is congruent, climate the two lines room parallel. |

Theorem 3-6 Consecutive angle (converse) | If two lines in a aircraft are reduced by a transversal so the a pair of consecutive interior angles is supplementary, then the lines space parallel. |

Theorem 3-8 Perpendicular present (converse) | In a plane, if two lines space perpendicular come the very same line, climate they space parallel. |

Theorem 3-7 Alt Int angle (converse) | If two lines in a aircraft are cut by a transversal so the a pair of alternating interior angles is congruent, climate the 2 lines room parallel. |

Postulate 3-2 Parallel Postulate | Two nonvertical lines have actually the exact same slope if and also only if they space parallel. |

Postulate 3-3 Perpendicular Postulate | Two nonvertical lines space perpendicular if and also only if the product of their slopes is -1. |

Theprem 2-1 Segment Congruence | Congruence of segment is reflexive, symmetric, and transitive |

Theorem 2-2 LP complement Theorem | If 2 angle for a direct pair, climate they are supplementary angles. |

Theorem 2-3 edge Congruence | Congruence of angles is reflexive, symmetric, and also transitive. |

Theorem 2-4 Supplementary Angles | Angles supplementary come the exact same angle or to congruent angles are congruent. See more: All About Ice Cream: Difference Between New York Style Vanilla Ice Cream 1Gl |

Theorem 2-5 security Angles | Angles complementary come the exact same angle or come congruent angles space congruent. |