Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.

Normal Size Small Size show me how

Normal Size Small Size show me how

# Chapter 6

### Polygons, Parallelograms, Rhombi, Squares, Kites, Trapezoids

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

Rectangle | parallelogram with four right angles |

Properties of a Rectangle | opposite sides are congruent; opposite angles are congruent; consecutive angles are supplementary; diagonals bisect each other; diagonals are congruent, opposite sides are parallel, 4 right angles |

Rhombus | Rhombus is a parallelogram with 4 congruent sides |

Properties of a Rhombus | opposite sides are congruent; opposite angles are congruent; consecutive angles are supplementary; diagonals bisect each other; diagonals are perpendicular; diagonals bisect each pair of opposite angles. DIAGONALS ARE NOT CONGRUENT |

Properties of a Square | opposite sides are congruent; opposite angles are congruent; consecutive angles are supplementary; diagonals bisect each other; diagonals are congruent; diagonals are perpendicular; diagonals bisect each pair of opposite angles. |

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

isosceles trapezoid | trapezoid whose nonparallel sides are congruent |

Properties of a Trapezoid | angles along the leg add to 180 degrees; all four angles add to 360 degrees; if the trapezoid is isosceles, then the base angles are equal and the diagonals are congruent. |

Kite | a kite is a quadrilateral with two pairs of consecutive sides congruent and NO opposite sides congruent. A kite has NO parallel sides, so a kite is NOT a parallelogram. |

Properties of a Kite | all four angles add up to 360 degrees; diagonals are perpendicular; one pair of opposite angles are congruent; no parallel sides. At the short diagonal, the angles are congruent. At the long diagonal, the diagonals are bisected. |

Trapezoid Midsegment Theorem | The midsegment of a trapezoid is parallel to each base and its measure is one half the sum of the lengths of the bases. M=1/2 (base one + base two) |

Polygons | a closed figure that has vertices, sides, angles and exterior angles. |

How do you name a polygon? | By listing the vertices in order around the polygon. |

Diagonal | a segment connecting 2 nonconsecutive vertices of a polygon. |

Convex polygon | polygon where NO diagonal goes outside the figure |

Concave polygon | Polygons where ANY diagonal goes outside the figure. Concave polygons "cave" in. |

3 sided polygon | triangle |

4 sided polygon | quadrilateral |

5 sided polygon | pentagon |

6 sided polygon | hexagon |

7 sided polygon | heptagon |

8 sided polygon | octagon |

9 sided polygon | nonagon |

10 sided polygon | decagon |

12 sided polygon | dodecagon |

angle sums of polygons | number of triangles formed by diagonals from one vertex |

interior angle sum theorem | the sum of the measures of the angles in a convex polygon with n sides is (n-2)180 |

exterior angle sum theorem | the sum of the measures of the exterior angles of ANY convex polygon, one at each vertex is 360. |

regular polygons | a polygon that is BOTH equilateral and equiangular. IF you see the word regular with a polygon, you can divide by the number of sides to find the individual angle measures. |

Parallelogram | a quadrilateral with BOTH pairs of opposite sides parallel. Abbreviation: //gram |

Properties of Parallelograms | opposite sides are congruent; opposite angles are congruent; consecutive angles are supplementary; diagonals bisect each other. |

Theorem 6.9 | If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. |

Theorem 6.10 | If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. |

Theorem 6.11 | If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a //gram. |

Theorem 6.12 | If one pair of opposite sides of a quadrilateral is BOTH congruent AND parallel, then the quadrilateral is a //gram. |

Created by:
amgeometry