Consider the squares below:
If you were to take the first square, cut it in half along the dotted line, and then switch the two halves, the square would look exactly the same as it did to start with. Similarly, if you were to cut any of the other three squares in half along the dotted line and then switch the two halves, the squares would not look any different than they did to start with. One way that you can test this idea is by printing this page, cutting out the squares, and folding
along the dotted lines. If they two halves "line up" perfectly, then the square is symmetric about your line of fold.
The examples above showed that the squares have what is called reflectional symmetry. But, the square also has what is called rotational symmetry. If you cut out
the square below and place it on a flat surface, place a pen or pencil on the
point in the center of the square, and rotate that square 90, 180, or 270
degrees clockwise or counterclockwise, the square will look exactly the same as
it did before you rotated it.
JavaSketchPad pages are provided for you to explore symmetry
with quadrilaterals and pentagons. Move the red points until the original
figure and the reflection image are superimposed (i.e., when they figure and
image are on top of each other). When you have accomplished this the reflection
line is now the axis or line of symmetry for the figure.