Goals of  the Unit

1. understand important properties of symmetry
2. recognize and describe symmetries of figures
3. use tools to examine symmetries and transformations
4. make figures with specified symmetries
5. identify a basic design element that can be used with a transformation to replicate a given design
6. perform symmetry transformations of figures, including reflections, translations, and rotations
7. examine and describe the symmetries of a design made from a figure and its image(s) under a symmetry transformation
8. give precise mathematical directions for performing reflections, rotations, and translations in terms of the effect of the transformation on points of the original figure
9. draw conclusions about a figure in terms of the effect of the transformation on points of the original figure based on what symmetry or symmetries the figure has
10. understand that figures with the same shape and size are congruent
11. use symmetry transformations to explore whether two figures are congruent
12. give examples of minimum sets of measures of angles and sides that will guarantee that two triangles are congruent
13. use congruence of triangles to explore congruence of two quadrilaterals
14. use symmetry and congruence to deduce properties of figures
15. write coordinate rules for specifying the image of a point under particular transformations
16. appreciate the power of transformational geometry in the real world

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Vocabulary

angle of rotation                            reflection                                        transformation
basic design element                    reflection symmetry                       translation
congruent                                      rotation                                           translation symmetry
congruent figures                         rotation symmetry
line reflection                                symmetry
line of symmetry                           tessellation