Elementary Geometry for College Students

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 p 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 Rene 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