Chapter Three
Transformational Geometry
Geometry is the study of those properties of a set which are preserved under a group of transformations on that set.
Felix Klein (1849–1925)

Section 3.1 -
Introduction      (Exercise 3.1)
Historical Overview

Section 3.2 -
Preliminary Definitions of a Transformation     (Exercises 3.2–3.5)
Model - An Analytic Model for the Euclidean Plane     (Exercises 3.6–3.18)
Model - Affine Transformation of the Euclidean Plane    (Exercises 3.19–3.23)

Section 3.3 -
Isometry      (Exercises 3.24–3.34)
Model - Collinearity for the Analytic Euclidean Plane    (Exercises 3.35–3.36)
Model - Isometry for the Analytic Euclidean Plane    (Exercises 3.37–3.45)

Section 3.4 -

Translation and Rotation   (Exercises 3.46–3.56)
Model - Translation and Rotation for the Analytic Euclidean Plane   (Exercises 3.57–3.66)

Section 3.5 -

Reflection and Glide Reflection   (Exercises 3.67–3.79)
Model - Reflection for the Analytic Euclidean Plane   (Exercises 3.80–3.85)

Section 3.6 -
Similarity Transformations   (Exercises 3.86–3.102)
Model - Similarity Transformation for the Analytic Euclidean Plane   (Exercises 3.103–3.107)

Section 3.7 - Model - Other Affine Transformations of the Euclidean Plane   (Exercises 3.108–3.110)

Chapter Three Exercises. Exercises from all the sections.
Solutions.
Solutions to selected exercises.
Self-Assessment Quizzes. Quizzes for all sections.