Preliminary Activity: Recall or find two familiar shapes that "exhibit symmetry" and two that do not. For each shape write a brief description as to why it does or does not exhibit symmetry.       When an object or picture is said to be symmetric, this usually implies that the object or picture is uniformly shaped or that it has a balanced arrangement. The word ``symmetry" comes from the ancient Greek word meaning ``the same measure." The Greeks believed that exhibiting symmetry or proportion was a virtue to strive for. Symmetry can be seen in architecture, nature, art, sports and games, and so many other places. Symmetry also plays a central role in mathematics.        Consider the following items. Are they symmetric? If an item is symmetric, what are the characteristics that make it so? If an item is not symmetric, what are the characteristics that prevent it from being so?