Transformational Plane Geometry (Textbooks in Mathematics)

Designed for a one-semester course at the junior undergraduate level, Transformational Plane Geometry takes a hands-on, interactive approach to teaching plane geometry. The book is self-contained, defining basic concepts from linear and abstract algebra gradually as needed.The text adheres to the National Council of Teachers of Mathematics Principles and Standards for School Mathematics and the Common Core State Standards Initiative Standards for Mathematical Practice. Future teachers will acquire the skills needed to effectively apply these standards in their classrooms. Following Felix Klein's Erlangen Program, the book provides students in pure mathematics and students in teacher training programs with a concrete visual alternative to Euclid's purely axiomatic approach to plane geometry. It enables geometrical visualization in three ways: Key concepts are motivated with exploratory activities using software specifically designed for performing geometrical constructions, such as Geometer's Sketchpad.Each concept is introduced synthetically (without coordinates) and analytically (with coordinates).Exercises include numerous geometric constructions that use a reflecting instrument, such as a MIRA.After reviewing the essential principles of classical Euclidean geometry, the book covers general transformations of the plane with particular attention to translations, rotations, reflections, stretches, and their compositions. The authors apply these transformations to study congruence, similarity, and symmetry of plane figures and to classify the isometries and similarities of the plane. MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict Front Cover 1 Dedication 9 Contents 11 Foreword 13 Preface 21 Authors 25 Chapter 1 - Axioms of Euclidean Plane Geometry 27 Chapter 2 - Theorems of Euclidean Plane Geometry 43 Chapter 3 - Introduction to Transformations, Isometries, and Similarities 59 Chapter 4 - Translations, Rotations, and Reflections 71 Chapter 5 - Compositions of Translations, Rotations, and Reflections 99 Chapter 6 - Classification of Isometries 133 Chapter 7 - Symmetry of Plane Figures 159 Chapter 8 - Similarity 195 Appendix - Hints and Answers to Selected Exercises 217 Bibliography 233 Back Cover 235 This text provides a one-semester introduction to transformational geometry based on Klein' s Erlangen Program, which offers an alternative to Euclid' s axiomatic/synthetic approach. The authors consider two families of transformations: isometries (distance-preserving transformations), including the translations, rotations, reflections, and glide reflections; and plane similarities, including the isometries, stretches, stretch rotations, and stretch reflections. The book helps students understand congruence ..