# rectangle

Rectangle^{}.
A quadrilateral^{} whose four angles are equal, that is, whose 4 angles are equal to ${90}^{\circ}$.

*Any rectangle is a parallelogram ^{}.*

This follows from angles $\mathrm{\angle}BAD$ and $\mathrm{\angle}ADC$ adding up ${180}^{\circ}$.

Since parallelograms have their opposite sides equal, so do rectangles. In the picture, $AB=CD$ and $BC=DA$.

Rectangles are the only parallelograms to be also cyclic (since opposite angles add up ${180}^{\circ}$.

Notice that every square is also a rectangle, but there are rectangles that are not squares

Rectangles have their two diagonals equal (since triangles $ABC$ and $ABD$ are congruent), A nice result following from this is that the quadrilateral obtained by joining the midpoints^{} of the sides is a rhombus^{}.

Since $PQ$ joins midpoints of sides in triangle $ABC$, we have $PQ=CA/2$. Similarly we have $RS=CA/2$, $QR=BD/2$ and $SP=BD/2$ and thus the sides of quadrilateral $PQRS$ are all equal, in other words, $PQRS$ is a rhombus.

Title | rectangle |
---|---|

Canonical name | Rectangle |

Date of creation | 2013-03-22 12:02:29 |

Last modified on | 2013-03-22 12:02:29 |

Owner | drini (3) |

Last modified by | drini (3) |

Numerical id | 6 |

Author | drini (3) |

Entry type | Definition |

Classification | msc 51-00 |

Related topic | Quadrilateral |

Related topic | Parallelogram |

Related topic | Rhombus |

Related topic | ParallelogramLaw |

Related topic | Square |