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• Overview
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• Table of Contents

Table of Contents

Note: Each chapter concludes with a Summary, Review Exercises, and a Chapter Test.
1. Line and Angle Relationships
1.1 Sets, Statements, and Reasoning
1.2 Informal Geometry and Measurement
1.3 Early Definitions and Postulates
1.4 Angles and Their Relationships
1.5 Introduction to Geometric Proof
1.6 Relationships: Perpendicular Lines
1.7 The Formal Proof of a Theorem
Perspective on History: The Development of Geometry
Perspective on Application: Patterns
2. Parallel Lines
2.1 The Parallel Postulate and Special Angles
2.2 Indirect Proof
2.3 Proving Lines Parallel
2.4 The Angles of a Triangle
2.5 Convex Polygons
2.6 Symmetry and Transformations
Perspective on History: Sketch of Euclid
Perspective on Application: Non-Euclidian Geometrics
3. Triangles
3.1 Congruent Triangles
3.2 Corresponding Parts of Congruent Triangles
3.3 Isosceles Triangles
3.4 Basic Constructions Justified
3.5 Inequalities in a Triangle
Perspective on History: Sketch of Archimedes
Perspective on Application: Pascal's Triangle
4. Quadrilaterals
4.1 Properties of a Parallelogram
4.2 The Parallelogram and Kite
4.3 The Rectangle, Square, and Rhombus
4.4 The Trapezoid
Perspective on History: Sketch of Thales
Perspective on Application: Square Numbers as Sums
5. Similar Triangles
5.1 Ratios, Rates, and Proportions
5.2 Similar Polygons
5.3 Proving Triangles Similar
5.4 The Pythagorean Theorem
5.5 Special Right Triangles
5.6 Segments Divided Proportionately
Perspective on History: Ceva's Proof
Perspective on Application: An Unusual Application of Similar Triangles
6. Circles
6.1 Circles and Related Segments and Angles
6.2 More Angle Relationships in the Circle
6.3 Line and Segment Relationships in the Circle
6.4 Some Constructions and Inequalities for the Circle
6.5 Locus of Points
6.6 Concurrence of Lines
Perspective on History: The Value of π
Perspective on Application: The Nine-Point Circle
7. Areas of Polygons and Circles
7.1 Area and Initial Postulates
7.2 Perimeter and Area of Polygons
7.3 Regular Polygons and Area
7.4 Circumference and Area of a Circle
7.5 More Area Relationships in the Circle
Perspective on History: Sketch of Pythagoras
Perspective on Application: Another Look at the Pythagorean Theorem
8. Surfaces and Solids
8.1 Prisms, Area, and Volume
8.2 Pyramids, Area, and Volume
8.3 Cylinders and Cones
8.4 Polyhedrons and Spheres
Perspective on History: Sketch of René Descartes
Perspective on Application: Birds in Flight
9. Analytic Geometry
9.1 The Rectangular Coordinate System
9.2 Graphs of Linear Equations and Slope
9.3 Preparing to Do Analytic Proofs
9.4 Analytic Proofs
9.5 Equations of Lines
Perspective on History: The Banach-Tarski Paradox
Perspective on Application: The Point-of-Division
10. Introduction to Trigonometry
10.1 The Sine Ratio and Applications
10.2 The Cosine Ratio and Applications
10.3 The Tangent Ratio and Other Ratios
10.4 Applications to Acute Triangles
Perspective on History: Sketch of Plato
Perspective on Application: Radian Measuer of Angles
Appendices
A. Algebra Review
B. Summary of Constructions, Postulates, and Theorems and Corollaries
Answers
Selected Exercises and Proofs