Elementary geometry for college students [electronic resource] / Daniel C. Alexander, Geralyn M. Koeberlein.

Includes index.

Chapter 1 Line and Angle Relationships1.1 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: Perpindicular Lines 1.7 The Formal Proof of a Theorem PERSPECTIVE ON HISTORY: The Development of Geometry PERSPECTIVE ON APPLICATION: Patterns Summary Review Exercises Chapter TestChapter 2 Parallel Lines2.1 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-Euclidean Geometries Summary Review Exercises Chapter TestChapter 3 Triangles3.1 Congruent Triangles 3.2 Correspondening 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 Summary Review Exercises Chapter TestChapter 4 Quadrilaterals4.1 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 Summary Review Exercises Chapter TestChapter 5 Similar Triangles5.1 Ratios, Rates and Proportions 5.2 Similar Polygons 5.3 Proving Triangles Similar 5.4 The Pythagorean Theory 5.5 Special Right Triangles 5.6 Segments Divided Proportionally PERSPECTIVE ON HISTORY: Ceva's Proof PERSPECTIVE ON APPLICATION: An Unusual Application of Similar Triangles Summary Review Exercises Chapter TestChapter 6 Circles6.1 Circles and Related Segments and Angles 6.2 More Angle Measures in the Circle 6.3 Line and Segment Relationships in the Circle 6.4 Some Construction and Inequalities in the Circle PERSPECTIVE ON HISTORY: Circumference of the Earth PERSPECTIVE ON APPLICATION: Sum of the Interior Angles of a Polygon Summary Review Exercises Chapter Test Chapter 7 Locus and Concurrence7.1 Locus of Points 7.2 Concurrence of Lines 7.3 More About Regular Polygons PERSPECTIVE ON HISTORY: The Value of p (Pi) PERSPECTIVE ON APPLICATION: The Nine-Point Circle Summary Review Exercises Chapter TestChapter 8 Areas of Polygons and Circles8.1 Areas and Initial Postulates 8.2 Perimeter and Area of Polygons 8.3 Regular Polygons and Area 8.4 Circumference and Area of a Circle 8.5 More Area Relationships in the Circle PERSPECTIVE ON HISTORY: Sketch of Pythagoras PERSPECTIVE ON APPLICATION: Another Look at the Pythagorean Theorem Summary Review Exercises Chapter Test Chapter 9 Surfaces and Solids9.1 Prisms, Area, and Volume 9.2 Pyramids, Area, and Volume 9.3 Cylinders and Cones 9.4 Polyhedrons and Spheres PERSPECTIVE ON HISTORY: Sketch of Rene Descartes PERSPECTIVE ON APPLICATION: Birds in Flight Summary Review Exercises Chapter TestChapter 10 Analytical Geometry10.1 The Rectangular Coordinate System 10.2 Graphs of Linear Equations and Slope 10.3 Preparing to do Analytic Proofs 10.4 Analytic Proofs 10.5 Equations of Lines 10.6 A Three-Dimensional Coordinate System PERSPECTIVE ON HISTORY: The Banach-Tarski Paradox PERSPECTIVE ON APPLICATION: The Point-of-Division Formulas Summary Review Exercises Chapter Test Chapter 11 Introduction to Trigonometry11.1 The Sine Ratio and Applications 11.2 The Cosine Ratio and Applications 11.3 The Tangent Ratio and Other Ratios 11.4 Applications with Acute Triangles PERSPECTIVE ON HISTORY: Sketch of Plato PERSPECTIVE ON APPLICATION: Radian Measure of Angles Summary Review Exercises Chapter TestAppendix A: Algebra ReviewAppendix B: Summaries of Constructions, Postulates, Theorems, and Corollaries.

Explores the important principles and real-world applications of plane, coordinate, and solid geometry. Strongly influenced by both NCTM and AMATYC standards, this book includes intuitive, inductive, and deductive experiences in its explorations.