![]() They can be reset by clicking the icon at the top right.Ĭonvention: in the figures, the orange polygon represents the original figure (the pre-image) the grey polygon(s) its image after the first reflection(s) the indigo polygon the final image.ĭownload all the GeoGebra files(plus bonus files!) Definitions and Assumptionsįor a definition of reflection, the construction assumptions, and the assumption that reflections preserve distance and angle measure, see TCS1 pp. Interaction! I made the interactive figures in GeoGebra. Instead, I will refer to them using the abbreviations in parentheses above. I will not duplicate the material found there. Depending on your background, you may benefit from working through the following before tackling this paper: Grades 8-9: Isometries | Congruence and Similarity, Lesson 1 Grades 9-10: Triangle Congruence and Similarity: v.1 (TCS1) | v.2 (TCS2) Grades 11-12: Isometries of the Plane (IP) In fact, the last three items are essential prerequisites to this article. You can find articles, lessons, and activities in transformational geometry here. In particular, it is necessary to know about the glide reflection. Prerequisites: Of course, the proof assumes some familiarity with isometries (aka rigid motions). It is largely based on Richard Brown's Transformational Geometry, though his proof is incomplete and in my opinion unnecessarily complicated. Who: This write-up is intended for teachers and curriculum developers, though it follows an outline I successfully implemented with 11th and 12th graders in my Space elective. Along the way, we will see a number of interesting results about rigid motions. To put it another way: given any two congruent figures in the plane, one is the image of the other in one of these four transformations. ![]() ![]() What: This is a proof that any isometry of the plane is one of these four: reflection, translation, rotation, or glide reflection. Three Reflections: Parallel or Concurrent Lines. ![]()
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