# Geometry 2

rename
Updated
2009-02-28 17:18

Shape | Properties |
---|---|

Triangle | A 3-sided Polygon in which any 3 sides a,b,c satisfy a+b>=c. |

Triangle | A 3-sided Polygon where all internal angles A,B,C total to 180 degrees. |

Triangle | A 3-sided Polygon in which the 3 sides a,b,c and 3 internal angles A,B,C satisfy the Law of Sines: a/sin(A)=b/sin(B)=c/sin(C). |

Triangle | A 3-sided Polygon in which any 3 sides a,b,c and the 3 internal angles A,B,C opposite them satisfy the Law of Cosines: c ^{2} = a^{2} - 2 a b cos(C) + b^{2}. |

Equilateral Triangle | A Triangle with all sides a,b,c the same length and all internal angles A,B,C equal to 60 degrees. |

Isosceles Triangle | A Triangle with 2 sides a,b the same length and the 2 internal angles A,B opposite these sides the same measure. |

Right Triangle | A Triangle in which the largest internal angle is 90 degrees. |

Right Triangle | A Triangle in which the 3 sides a,b,c satisfy the Pythagorean Theorem: a ^{2}+b^{2}=c^{2} where c is thehypotenuse (the longest side). |

Right Isosceles Triangle | A Triangle with one 90 degree and two 45 degree internal angles. |

Right Triangle | A Triangle with sides in the ratio 3:4:5. |

Right Triangle | A Triangle with sides in the ratio 5:12:13. |

Right Triangle | A Triangle with sides in the ratio of a Pythagorean Triple. |

See Pythagorean Theorem for a list of Pythagorean Triples.

Shape | Properties |
---|---|

Rectangle | A 4-sided Polygon with all internal angles equal to 90 degrees. |

Square | A Rectangle with all sides the same length. |

Trapezoid | A 4-sided Polygon with 2 sides parallel and 2 sides not parallel. |

Rhombus | A 4-sided Polygon shaped like a diamond on a deck of cards. |

Rhombus | A 4-sided Polygon where all sides are the same length and opposite angles have the same measure. |

Kite | A 4-sided Polygon where 2 sets of adjacent sides have the same length and 1 set of opposite angles have the same measure. It has one axis of symmetry. It is like 2 isosceles triangles end to end. |

Parallelogram | A 4-sided Polygon with opposite sides the same length and opposite angles the same measure. |

Parallelogram | A 4-sided Polygon with opposite sides parallel to each other. |

Parallelogram | Could be a Rectangle, Square, or Rhombus. |

Quadrilateral | Could be a Trapezoid, Kite, or Parallelogram. |

Quadrilateral | A 4-sided Polygon where all internal angles total to 360 degrees. |

Pentagon | A 5-sided Polygon where all internal angles total to 540 degrees. |

Hexagon | A 6-sided Polygon where all internal angles total to 720 degrees. |

Octagon | An 8-sided Polygon where all internal angles total to 1080 degrees. |

Polygon | An n-sided figure where all external angles total to 360 degrees and all internal angles total to 180 n - 360 degrees. |

Circle | All points equidistant from a central point in 2-dimensions. |

Sphere | All points equidistant from a central point in 3-dimensions. |

Fill in the blanks for the following:

Statement | Missing Words |
---|---|

Two triangles are congruent if each has ___ | all 3 sides and all 3 internal angles the same. |

Two triangles are congruent if each has ___ | all 3 sides the same (SSS). |

Two triangles are congruent if each has ___ | 1 side and any 2 internal angles the same (ASA or AAS). |

Two triangles are congruent if each has ___ | 1 internal angle and the 2 sides connected by this angle the same (SAS). |

Two triangles are not necessarily congruent if each has ___ | 1 internal angle and two sides (one adjacent to the angle and one opposite the angle) the same (SSA). |

Two triangles are similar but not necessarily congruent if each has ___ | all 3 internal angles the same (AAA). |

See Geometry, Math, or http://www.mathsisfun.com/geometry/plane-geometry.html for more.

See http://www.mathsisfun.com/numbers/pythagorean-triples.html for Pythagorean Triples.

See http://www.mathsisfun.com/algebra/trig-solving-triangles.html for congruent triangles.