# Geometry
## Contents

This book is part of a series on Geometry:
Geometry for Elementary School High School Geometry Geometry Trigonometry
* Cover
* Authors
* For Contributors

### Preface

Chapter 0: The World Around Us

### Unit 1: Elements of Geometry

Chapter 1: An Introduction to Geometry Chapter 2: Ruler and Compass Constructions Chapter 3: Cartesian Geometry Chapter 4: Rigid Motions

### Unit 2: Geometric Proofs

Chapter 5: Lines on a Plane Chapter 6: Congruence Theorems Chapter 7: Triangle Theorems Chapter 8: Quadrilateral Theorems Chapter 9: Polygons Chapter 10: Similarity Theorems Chapter 11: Inequalities in Geometry Chapter 12: Circle Theorems

### Unit 3: Spatial Geometry

Chapter 13: Three-Dimensional Geometry Chapter 14: Non-Euclidean Geometry

### Unit 4: Geometric Measurement

Chapter 15: Trigonometry Chapter 16: Area and Perimeter Chapter 17: Surface Area, Volume, Mass, and Density Chapter 18: Geometric Probability

### Unit 5: Advanced Geometry

Chapter 19: Projective Geometry Chapter 20: Topology Chapter 21: Affine Geometry Chapter 22: Crystallography Chapter 23: Neutral Geometry Chapter 24: Inversive Geometry

## High School Geometry

The outline of topics reflects the California curriculum content standards.

### Navigation

* Geometry Main Page
* Motivation
* Introduction
* Geometry/Chapter 1 - HS Definitions and Reasoning (Introduction)
** Geometry/Chapter 1/Lesson 1 Introduction
** Geometry/Chapter 1/Lesson 2 Reasoning
** Geometry/Chapter 1/Lesson 3 Undefined Terms
** Geometry/Chapter 1/Lesson 4 Axioms/Postulates
** Geometry/Chapter 1/Lesson 5 Theorems
** Geometry/Chapter 1/Vocabulary Vocabulary
* Geometry/Chapter 2 Proofs
* Geometry/Chapter 3 Logical Arguments
* Geometry/Chapter 4 Congruence and Similarity
* Geometry/Chapter 5 Triangle: Congruence and Similiarity
* Geometry/Chapter 6 Triangle: Inequality Theorem
* Geometry/Chapter 7 Parallel Lines, Quadrilaterals, and Circles
* Geometry/Chapter 8 Perimeters, Areas, Volumes
* Geometry/Chapter 9 Prisms, Pyramids, Spheres
* Geometry/Chapter 10 Polygons
* Geometry/Chapter 11 $\mathbb {R} ,\mathbb {R} ^{2},\mathbb {R} ^{3}$
* Geometry/Chapter 12 Angles: Interior and Exterior
* Geometry/Chapter 13 Angles: Complementary, Supplementary, Vertical
* Geometry/Chapter 14 Pythagorean Theorem: Proof
* Geometry/Chapter 15 Pythagorean Theorem: Distance and Triangles
* Geometry/Chapter 16 Constructions
* Geometry/Chapter 17 Coordinate Geometry
* Geometry/Chapter 18 Trigonometry
* Geometry/Chapter 19 Trigonometry: Solving Triangles
* Geometry/Chapter 20 Special Right Triangles
* Geometry/Chapter 21 Chords, Secants, Tangents, Inscribed Angles, Circumscribed Angles
* Geometry/Chapter 22 Rigid Motion
* Geometry/Appendix A Formulae
* Geometry/Appendix B Answers to problems
* Appendix C. Geometry/Postulates & Definitions
* Appendix D. Geometry/The SMSG Postulates for Euclidean Geometry

## General Geometry
### Navigation

* Geometry
* Part I—Euclidean Geometry:
** Chapter 1. Geometry/Points, Lines, Line Segments and Rays
** Chapter 2. Geometry/Angles
** Chapter 3. Geometry/Properties
** Chapter 4. Geometry/Inductive and Deductive Reasoning
** Chapter 5. Geometry/Proof
** Chapter 6. Geometry/Five Postulates of Euclidean Geometry
** Chapter 7. Geometry/Vertical Angles
** Chapter 8. Geometry/Parallel and Perpendicular Lines and Planes
** Chapter 9. Geometry/Congruency and Similarity
** Chapter 10. Geometry/Congruent Triangles
** Chapter 11. Geometry/Similar Triangles
** Chapter 12. Geometry/Quadrilaterals
** Chapter 13. Geometry/Parallelograms
** Chapter 14. Geometry/Trapezoids
** Chapter 15. Geometry/Circles/Radii, Chords and Diameters
** Chapter 16. Geometry/Circles/Arcs
** Chapter 17. Geometry/Circles/Tangents and Secants
** Chapter 18. Geometry/Circles/Sectors
** Appendix A. Geometry/Postulates & Definitions
** Appendix B. Geometry/The SMSG Postulates for Euclidean Geometry
* Part II—Coordinate Geometry:
** Geometry/Synthetic versus analytic geometry
* Two and Three-Dimensional Geometry and Other Geometric Figures
** Geometry/Perimeter and Arclength
** Geometry/Area
** Geometry/Volume
** Geometry/Polygons
** Geometry/Triangles
** Geometry/Right Triangles and Pythagorean Theorem
** Geometry/Polyominoes
** Geometry/Ellipses
** Geometry/2-Dimensional Functions
** Geometry/3-Dimensional Functions
** Geometry/Area Shapes Extended into 3rd Dimension
** Geometry/Area Shapes Extended into 3rd Dimension Linearly to a Line or Point
** Geometry/Polyhedras
** Geometry/Ellipsoids and Spheres
** Geometry/Coordinate Systems (currently incorrectly linked to Astronomy)
* Traditional Geometry:
** Geometry/Topology
** Geometry/Hyperbolic and Elliptic Geometry
** Geometry/Projective Geometry
** Geometry/Neutral Geometry
** Geometry/Inversive Geometry
* Modern geometry
** Geometry/Unified Angles
** Geometry/Groups
** Geometry/Algebraic Geometry
** Geometry/Differential Geometry
** Geometry/Algebraic Topology
** Geometry/Noncommutative Geometry
* Geometry/An Alternative Way and Alternative Geometric Means of Calculating the Area of a Circle