Schaum's Outline of Geometry, 5th Edition | Schaum's Outline

Home >
Browse >
Schaum's Outline >
Schaum's Outline of Geometry, 5th Edition

Schaum's Outline of Geometry, 5th Edition

Authors: Christopher Thomas and Barnett Rich

Published: November 2012

eISBN: 9780071795418 0071795413 | ISBN: 9780071795401

Cover

Title Page

Copyright Page

Contents

Chapter 1 Lines, Angles, and Triangles

1.1 Historical Background of Geometry

1.2 Undefined Terms of Geometry: Point, Line, and Plane

1.3 Line Segments

1.4 Circles

1.5 Angles

1.6 Triangles

1.7 Pairs of Angles

Chapter 2 Methods of Proof

2.1 Proof by Deductive Reasoning

2.2 Postulates (Assumptions)

2.3 Basic Angle Theorems

2.4 Determining the Hypothesis and Conclusion

2.5 Proving a Theorem

Chapter 3 Congruent Triangles

3.1 Congruent Triangles

3.2 Isosceles and Equilateral Triangles

Chapter 4 Parallel Lines, Distances, and Angle Sums

4.1 Parallel Lines

4.2 Distances

4.3 Sum of the Measures of the Angles of a Triangle

4.4 Sum of the Measures of the Angles of a Polygon

4.5 Two New Congruency Theorems

Chapter 5 Parallelograms,Trapezoids, Medians, and Midpoints

5.1 Trapezoids

5.2 Parallelograms

5.3 Special Parallelograms: Rectangle, Rhombus, and Square

5.4 Three or More Parallels; Medians and Midpoints

Chapter 6 Circles

6.1 The Circle; Circle Relationships

6.2 Tangents

6.3 Measurement of Angles and Arcs in a Circle

Chapter 7 Similarity

7.1 Ratios

7.2 Proportions

7.3 Proportional Segments

7.4 Similar Triangles

7.8 Mean Proportionals in a Right Triangle

7.9 Pythagorean Theorem

7.10 Special Right Triangles

Chapter 8 Trigonometry

8.1 Trigonometric Ratios

8.2 Angles of Elevation and Depression

Chapter 9 Areas

9.1 Area of a Rectangle and of a Square

9.2 Area of a Parallelogram

9.3 Area of a Triangle

9.4 Area of a Trapezoid

9.5 Area of a Rhombus

9.6 Polygons of the Same Size or Shape

9.7 Comparing Areas of Similar Polygons

Chapter 10 Regular Polygons and the Circle

10.1 Regular Polygons

10.2 Relationships of Segments in Regular Polygons of 3, 4, and 6 Sides

10.3 Area of a Regular Polygon

10.4 Ratios of Segments and Areas of Regular Polygons

10.5 Circumference and Area of a Circle

10.6 Length of an Arc; Area of a Sector and a Segment

10.7 Areas of Combination Figures

Chapter 11 Locus

11.1 Determining a Locus

11.2 Locating Points by Means of Intersecting Loci

11.3 Proving a Locus

Chapter 12 Analytic Geometry

12.1 Graphs

12.2 Midpoint of a Segment

12.3 Distance Between Two Points

12.4 Slope of a Line

12.5 Locus in Analytic Geometry

12.6 Areas in Analytic Geometry

12.7 Proving Theorems with Analytic Geometry

Chapter 13 Inequalities and Indirect Reasoning

13.1 Inequalities

13.2 Indirect Reasoning

Chapter 14 Improvement of Reasoning

14.1 Definitions

14.2 Deductive Reasoning in Geometry

14.3 Converse, Inverse, and Contrapositive of a Statement

14.4 Partial Converse and Partial Inverse of a Theorem

14.5 Necessary and Sufficient Conditions

Chapter 15 Constructions

15.1 Introduction

15.2 Duplicating Segments and Angles

15.3 Constructing Bisectors and Perpendiculars

15.4 Constructing a Triangle

15.5 Constructing Parallel Lines

15.6 Circle Constructions

15.7 Inscribing and Circumscribing Regular Polygons

15.8 Constructing Similar Triangles

Chapter 16 Proofs of Important Theorems

16.1 Introduction

16.2 The Proofs

Chapter 17 Extending Plane Geometry into Solid Geometry

17.1 Solids

17.2 Extensions to Solid Geometry

17.3 Areas of Solids: Square Measure

17.4 Volumes of Solids: Cubic Measure

Chapter 18 Transformations

18.1 Introduction to Transformations

18.2 Transformation Notation

18.3 Translations

18.4 Reflections

18.5 Rotations

18.6 Rigid Motions

18.7 Dihilations

Chapter 19 Non-Euclidean Geometry

19.1 The Foundations of Geometry

19.2 The Postulates of Euclidean Geometry

19.3 The Fifth Postulate Problem

19.4 Different Geometries

Formulas for Reference

Answers to Supplementary Problems

Index