Symmetry of two-dimensional shapes

The  exercise appears under the Geometry Math Mission. This exercise explores the symmetry properties of two-dimensional geometric figures.

Types of Problems
There are three types of problems in this exercise:


 * 1) Draw the shape based on the symmetry descriptions: This problem has a coordinate grid and some points. The student is asked to move the points to design a geometric shape based on some symmetry conditions.So2ds1.png
 * 2) Determine the descriptions true about the diagram: This problem has a geometric shape displayed on a coordinate plane. The student is asked to select all of the symmetry conditions that are true about the diagram from a multiple select list.So2ds2.png
 * 3) Determine the shapes with the desired symmetry: This problem has several potential shapes that may hold a specific type of symmetry. The student is asked to select all shapes that have that symmetry from a multiple select list.So2ds3.png

Strategies
Knowledge of vocabulary terms and a discerning geometric eye are encouraged to ensure success on this exercise.
 * 1) A reflection symmetry can be recognized by placing a piece of paper over "half" the picture and seeing an identical (but flipped) shape through the paper.
 * 2) A rotation symmetry can be recognized by turning the table, ipad, or computer screen about a point.
 * 3) When making pictures, graph the specific points first, then use any reflection symmetry conditions to fix those points next. The remaining points should fill in more easily after the reflection points are placed.

Real-life Applications

 * 1) A firm understanding of transformations is necessary for understanding some of the more intricate concepts in non-Euclidean geometry (a possible model of the universe).
 * 2) Transformations have applications in art and architecture.