## Table of Contents

1. Introduction

1.1 Basic geometric objects

1.2 More about angles

1.3 Congruent objects and bisectors

1.4 Common relationships between angles

1.5 Proofs: Introduction

1.6 GeoGebra: Introduction

2. Triangles

2.1 Triangle basics

2.2 The Pythagorean theorem

2.3 Congruent triangles

2.4 Similar triangles

2.5 Special right triangles

2.6 Proofs: Triangles

2.7 GeoGebra: Triangles

3. Quadrilaterals

3.1 Quadrilateral basics

3.2 Diagonals

3.3 Proofs: Quadrilaterals

3.4 Geogebra: Quadrilaterals

4. Polygons

4.1 Classifying polygons

4.2 Theorems about polygons

4.3 GeoGebra: Polygons

5. Area and Perimeter

5.1 Perimeter

5.2 Area

5.3 Complex shapes

5.4 GeoGebra: Area and perimeter

6. Circles

6.1 Definitions and terminology

6.2 Circumference and area

6.3 Sectors and arc length

6.4 Theorems about circles

6.5 Proofs: Circles

6.6 GeoGebra: Circles

7. Volume and Surface Area

7.1 Volumes of common shapes

7.2 Volumes of cones and pyramids

7.3 Spheres

7.4 Surface area

8. Basic Trigonometry

8.1 Ratios in a right triangle

8.2 Finding unknown values

9. Analytic Geometry

9.1 Distance, midpoint, and slope

9.2 Transformations

9.3 Isometries and composition of transformations

9.4 Symmetry

9.5 Proofs: Analytic geometry

9.6 GeoGebra: Transformations

10. Non-Euclidean Geometries

10.1 Finite geometries

10.2 Taxicab geometry

10.3 Spherical geometry

10.4 Hyperbolic geometry

11. Appendix

11.1 Exponents and the order of operations

11.2 Linear equations

11.3 Rectangular coordinate system

11.4 Introduction to vectors

11.5 Geometry formulas

## What You’ll Find In This zyBook:

### More action with less text.

- Exceptionally interactive material on Euclidean and non-Euclidean geometries
- Hundreds of auto-graded activities such as question sets, animations, and challenge activities
- An interactive embedded GeoGebra applet for doing geometry constructions
- Interactive two-column proofs for Euclidean and non-Euclidean geometries

## The zyBooks Approach

### Less text doesn’t mean less learning.

This material provides an interactive approach to geometry. This release covers Euclidean plane geometry including two-column proofs for theorems on angles, triangles, quadrilaterals, and circles. The release also covers basic analytic geometry and non-Euclidean geometries, and reviews basic trigonometry. The non-Euclidean geometry chapter covers axiomatic proofs. Constructions are included in the zyBook using an interactive GeoGebra tool.

## Author

**Alan Bass**