ANOTHER LOOK AT SYMMETRY
Instructions
Symmetry is another attribute that we can use to classify shapes.
You have already discovered one type of symmetry – line symmetry.
Some shapes have line symmetry, others don’t. Some have more lines of symmetry than others do.
There is another type of symmetry. This GeoGebra lab activity will introduce this new form of symmetry.
Step 1. Experiment and Observe
On the GeoGebra workspace, there are two quadrilaterals that are identical. The quadrilateral on the right has a blue drag point that can be used to rotate the shape.
Use the MOVE tool 
to rotate the shape.
As soon as you begin to rotate the quadrilateral, the two shapes are no longer completely identical. But as you continue to rotate the shape, notice that at certain points in the rotation, the rotating shape will again look identical to the quadrilateral on the left. This shape has rotational symmetry. With rotational symmetry, the shape or image can be rotated to a point where it looks identical to the original.
As you make one complete rotation of the square, at how many points in this rotation are the shapes identical again? You should see four (counting the original position).
Step 2. Try Other Shapes
Use the MOVE GRAPHICS VIEW tool 
to move down the GeoGebra page.
Try the same experiment with the triangle, the trapezoid, and the rectangle.
Record how many times in a rotation the shapes are identical:
Quadrilateral __________Triangle __________Trapezoid __________Rectangle __________
If a shape can be completely rotated and there is only one point where it is identical to the original, then that shape does not have rotational symmetry. Do any of these shapes not have rotational symmetry?
to rotate the shape.
As soon as you begin to rotate the quadrilateral, the two shapes are no longer completely identical. But as you continue to rotate the shape, notice that at certain points in the rotation, the rotating shape will again look identical to the quadrilateral on the left. This shape has rotational symmetry. With rotational symmetry, the shape or image can be rotated to a point where it looks identical to the original.
As you make one complete rotation of the square, at how many points in this rotation are the shapes identical again? You should see four (counting the original position).
Step 2. Try Other Shapes
Use the MOVE GRAPHICS VIEW tool to move down the GeoGebra page.
Try the same experiment with the triangle, the trapezoid, and the rectangle.
Record how many times in a rotation the shapes are identical:
Quadrilateral __________Triangle __________Trapezoid __________Rectangle __________
If a shape can be completely rotated and there is only one point where it is identical to the original, then that shape does not have rotational symmetry. Do any of these shapes not have rotational symmetry?