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The first is that it is one of only four types of transformations that connect any two congruent figures in the plane see below. The second is that it is needed in the study of symmetry. Read an introduction to the glide reflection here. Epic proof that any isometry of the plane is one of these four: reflection, translation, rotation, or glide reflection, with interactive figures. Transformational Geometry Lost in Translation?

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Triangle Congruence and Similarity, v1 With Lew Douglas : Triangle Congruence and Similarity, v2 These documents are intended to support teachers and curriculum developers who are wrestling with the logical relationship between transformations and the congruence and similarity criteria. With Lew Douglas: Transformational Proof in High School Geometry updated: March This document is a logically coherent presentation of a substantial portion of a high school geometry course, based on geometric transformations.

Chapter 5 Compositions of Translations Rotations and Reflections.

Transformation geometry - Wikipedia

Chapter 6 Classification of Isometries. Chapter 7 Symmetry of Plane Figures. Chapter 8 Similarity. Appendix Hints and Answers to Selected Exercises. Transformational Plane Geometry Ronald N. Chapter 1 Axioms of Euclidean Plane Geometry.

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    Transformational Plane Geometry by Ronald N. Umble, Zhigang Han (Hardback, 2014)

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    Transformations - Reflection

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