Symmetry in Quadrilaterals Exploration

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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.