# Symmetry in Quadrilaterals Exploration

**Objective:**
Record the common features of various quadrilaterals. Some are alike and some are different with regard to these features. Introduce the concept of (bilateral) symmetry in a non-rigorous manner.

1. In the following table, indicate by Y (yes) or N (no) whether each of the figures * always* has the indicated property.

Quadrilateral | All sides congruent | Opposite sides congruent | Opposite sides parallel |
---|---|---|---|

Rectangle | |||

Parallelogram | |||

Trapezoid | |||

Rhombus | |||

Kite | |||

Square | |||

Any Quadrilateral |

2. In the following table, indicate by Y (yes) or N (no) whether each of the figures * always* has the indicated property.

Quadrilateral | All angles congruent | Opposite angles congruent | Has right angles |
---|---|---|---|

Rectangle | |||

Parallelogram | |||

Trapezoid | |||

Rhombus | |||

Kite | |||

Square | |||

Any Quadrilateral |

3. Draw the two diagonals of each of the figures. In the table indicate by Y and N whether the figure always has the indicated property of the diagonals.

Quadrilateral | Bisect each other | Are congruent | Meet at right angles |
---|---|---|---|

Rectangle | |||

Parallelogram | |||

Trapezoid | |||

Rhombus | |||

Kite | |||

Square | |||

Any Quadrilateral |

4. In how many ways can you fold a square so that one half matches the other half? (If you get a fold in the paper that you already had, don't count it again.) How many folds can you get in any rectangle so that one half matches the other half? The folds you are getting are called lines of symmetry. In the table record your results.

Quadrilateral | Number of Lines of Symmetry |
---|---|

Rectangle | |

Parallelogram | |

Trapezoid | |

Rhombus | |

Kite | |

Square | |

Any Quadrilateral |

**Handin:**
A sheet with answers to all questions.