Contents
1.5 Perpendiculars and Angle Bisectors
1.7 Solutions to Selected Exercises
2.6 Solutions to the Exercises
3.2 Parallel Lines and Similarity
3.3 Other Conditions Implying Similarity
3.7 Solutions to the Exercises
Chapter 4: Theorems of Ceva and Menelaus
4.1 Directed Distances, Directed Ratios
4.3 Applications of Ceva’s Theorem
4.4 Applications of Menelaus’ Theorem
4.6 Extended Versions of the Theorems
5.2 Applications of the Basic Properties
5.3 Other Formulae for the Area of a Triangle
5.4 Solutions to the Exercises
Chapter 6: Miscellaneous Topics
6.1 The Three Problems of Antiquity
6.2 Constructing Segments of Specific Lengths
6.3 Construction of Regular Polygons
6.7 The Steiner-Lehmus Theorem
6.9 Solutions to the Exercises
Part II: Transformational Geometry
Chapter 7: The Euclidean Transformations or Isometries
7.1 Rotations, Reflections, and Translations
7.2 Mappings and Transformations
7.3 Using Rotations, Reflections, and Translations
Chapter 8: The Algebra of Isometries
8.1 Basic Algebraic Properties
8.3 The Product of Reflections
Chapter 9: The Product of Direct Isometries
9.3 The Product of Two Translations
9.4 The Product of a Translation and a Rotation
9.5 The Product of Two Rotations
Chapter 10: Symmetry and Groups
11.4 Using Homotheties in Proofs
12.3 Tiling with Regular Polygons
12.4 Platonic and Archimedean Tilings
Part III: Inversive and Projective Geometries
Chapter 13: Introduction to Inversive Geometry
13.1 Inversion in the Euclidean Plane
13.2 The Effect of Inversion on Euclidean Properties
13.4 Compass-Only Constructions
Chapter 14: Reciprocation and the Extended Plane
14.2 The Projective Plane and Reciprocation
14.3 Conjugate Points and Lines
15.2 Applications of Cross Ratios
Chapter 16: Introduction to Projective Geometry
16.1 Straightedge Constructions
16.2 Perspectivities and Projectivities
16.3 Line Perspectivities and Line Projectivities
16.4 Projective Geometry and Fixed Points
16.5 Projecting a Line to Infinity