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# Chapter 8 Notecards

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

Diagonal | diagonal of a polygon is a segment that joins two nonconsecutive vertices |

Polygon Interior Angles Theorem | The sum of the measures of the interior angles of a convex n-gon is (n-2)180 |

Interior Angles of a Quadrilateral Corollary | The sum of the measures of the interior angles of a quadrilateral is 360 |

Polygon Exterior Angles Theorem | The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360. |

Parallelogram | a quadrilateral with both pairs of opposite sides parallel. |

Theorem 8.3 | if a quadrilateral is a parallelogram then its opposite sides are congruent |

Theorem 8.4 | if a quadrilateral is a parallelogram then its opposite angles are congruent |

Theorem 8.5 | if a quadrilateral is a parallelogram then its consecutive angles are supplementary |

Theorem 8.6 | if a quadrilateral is a parallelogram then its diagonals bisect each other |

Theorem 8.7 | if both pairs of opposite sides of a quadrilateral are congruent then the quadrilateral is a parallelogram |

Theorem 8.8 | if both pairs of opposite angles of a quadrilateral are congruent then the quadrilateral is a parallelogram |

Theorem 8.9 | if one pair of opposite sides of a quadrilateral are congruent and parallel then the quadrilateral is a parallelogram |

Theorem 8.10 | if the diagonals of a quadrilateral bisect each other then the quadrilateral is a parallelogram |

Rhombus | a parallelogram with four congruent sides |

Rectangle | a parallelogram with four right angles |

Square | a parallelogram with four congruent sides and four right angles. |

Rhombus Corollary | a quadrilateral is a rhombus if and only if it has four congruent sides |

Rectangle Corollary | a quadrilateral is a rectangle if and only if it has four right angles |

Square Corollary | a quadrilateral is a square if and only if it is a rhombus and a rectangle |

Theorem 8.11 | a parallelogram is a rhombus if and only if its diagonals are perpendicular |

Theorem 8.12 | a parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles |

Theorem 8.13 | a parallelogram is a rectangle if and only if its diagonals are congruent |

Trapezoid | a quadrilateral with exactly one pair of parallel sides |

Bases of a Trapezoid | The parallel sides are the bases and there is only two pairs of base angles. |

Legs of a Trapezoid | the nonparallel sides |

Theorem 8.14 | if a trapezoid is isosceles then each pair of base angles is congruent |

Theorem 8.15 | if a trapezoid has a pair of congruent base angles then it is an isosceles trapezoid |

Theorem 8.16 | a trapezoid is isosceles if and only if its diagonals are congruent |

Midsegment of a Trapezoid | the segment that connects the midpoints of its legs |

Midsegment Theorem for Trapezoids | the midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases |

Kite | a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent |

Theorem 8.18 | if a quadrilateral is a kite then its diagonals are perpendicular |

Theorem 8.19 | if a quadrilateral is a kite then exactly one pair of opposite angles are congruent |

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