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Transformational

G.G.54 Define, investigate, justify, and apply isometries in the Geometry plane (rotations, reflections, translations, glide reflections) Note: Use proper function notation.

G.G.55 Investigate, justify, and apply the properties that remain invariant under translations, rotations, reflections, and glide reflections

G.G.56 Identify specific isometries by observing orientation, numbers of invariant points, and/or parallelism

G.G.57 Justify geometric relationships (perpendicularity, parallelism, congruence) using transformational techniques (translations, rotations, reflections)

G.G.58 Define, investigate, justify, and apply similarities (dilations and the composition of dilations and isometries)

G.G.59 Investigate, justify, and apply the properties that remain invariant under similarities

G.G.60 Identify specific similarities by observing orientation, numbers of invariant points, and/or parallelism

G.G.61 Investigate, justify, and apply the analytical representations for translations, rotations about the origin of 90º and 180º, reflections over the lines x =0, y = 0, and y = x, and dilations centered at the origin


Useful Links to Symmetry and Transformations:

University of Georgia

Mathsnet Transformations

Drexel University Math Forums

Learning in Context

Introduction to Isometries