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# Geometry Vocabulary

### Theorems, axioms, postulates, properties in Geometry

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

Complementary angles | Two angles whose measures have a sum of 90o |

Supplementary angles | Two angles whose measures have a sum of 180o |

Theorem | A statement that can be proven |

Vertical Angles | Two angles formed by intersecting lines and facing in the opposite direction |

Transversal | A line that intersects two lines in the same plane at different points |

Corresponding angles | Pairs of angles formed by two lines and a transversal that make an F pattern |

Same-side interior angles | Pairs of angles formed by two lines and a transversal that make a C pattern |

Alternate interior angles | Pairs of angles formed by two lines and a transversal that make a Z pattern |

Congruent triangles | Triangles in which corresponding parts (sides and angles) are equal in measure |

Similar triangles | Triangles in which corresponding angles are equal in measure and corresponding sides are in proportion (ratios equal) |

Angle bisector | A ray that begins at the vertex of an angle and divides the angle into two angles of equal measure |

Segment bisector | A ray, line or segment that divides a segment into two parts of equal measure |

Legs of an isosceles triangle | The sides of equal measure in an isosceles triangle |

Base of an isosceles triangle | The third side of an isosceles triangle |

Equiangular | Having angles that are all equal in measure |

Perpendicular bisector | A line that bisects a segment and is perpendicular to it |

Altitude | A segment from a vertex of a triangle perpendicular to the line containing the opposite side |

Reflexive Property | A quantity is equal to itself |

Symmetric Property | If A = B, then B = A |

Transitive Property | If A = B and B = C, then A = C |

Addition Property of Equality | If A = B, then A + C = B + C |

Angle Addition Postulate | If a point lies on the interior of an angle, that angle is the sum of two smaller angles with legs that go through the given point |

Corresponding Angles Postulate | If a transversal intersects two parallel lines, the pairs of corresponding angles are congruent |

Parallel Postulate | Given a line and a point not on that line, there exists a unique line through the point parallel to the given line |

Alternate Exterior Angles Theorem | If a transversal intersects two parallel lines, then the alternate exterior angles are congruent. Converse: If a transversal intersects two lines and the alternate exterior angles are congruent, then the lines are parallel |

Alternate Interior Angles Theorem | If a transversal intersects two parallel lines, then the alternate interior angles are congruent. Converse: If a transversal intersects two lines and the alternate interior angles are congruent, then the lines are parallel |

Congruent Complements Theorem | If two angles are complements of the same angle (or of congruent angles), then the two angles are congruent |

Congruent Supplements Theorem | If two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent |

Right Angles Theorem | All right angles are congruent |

Same-Side Interior Angles Theorem | If a transversal intersects two parallel lines, then the interior angles on the same side are supplementary. Converse: If a transversal intersects two lines and the interior angles on the same side are supplementary, then the lines are parallel. |

Vertical Angles Theorem | If two angles are vertical angles, then they have equal measures |

Vertical Angles | the angles opposite each other when two lines cross |

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