Elementary Geometry for College Students

P. Preliminary Concepts. Sets and Geometry. Statements and Reasoning. Informal Geometry and Measurement. PERSPECTIVE ON HISTORY: Our Greek Heritage. PERSPECTIVE ON APPLICATION: ONE-TO-ONE Correspondence. Summary Review Exercises Chapter Test. 1. Line and Angle Relationships. Early Definitions and Postulates. Angles and Their Relationships. Introduction to Geometric Proof. Relationships: Perpendicular Lines. The Formal Proof of a Theorem. PERSPECTIVE ON HISTORY: The Development of Geometry. PERSPECTIVE ON APPLICATION: Patterns. Summary Review Exercises Chapter Test. 2. Parallel Lines. The Parallel Postulate and Special Angles. Indirect Proof. Proving Lines Parallel. The Angles of a Triangle. Convex Polygons. Symmetry and Transformations. PERSPECTIVE ON HISTORY: Sketch of Euclid. PERSPECTIVE ON APPLICATION: Non-Euclidean Geometries. Summary Review Exercises Chapter Test. 3. Triangles. Congruent Triangles. Corresponding Parts of Congruent Triangles. Isosceles Triangles. Basic Constructions Justified. Inequalities in a Triangle. PERSPECTIVE ON HISTORY: Sketch of Archimedes. PERSPECTIVE ON APPLICATION: Pascal's Triangle. Summary Review Exercises Chapter Test. 4. Quadrilaterals. Properties of a Parallelogram. The Parallelogram and Kite. The Rectangle, Square, and Rhombus. The Trapezoid. PERSPECTIVE ON HISTORY: Sketch of Thales. PERSPECTIVE ON APPLICATION: Square Numbers as Sums. Summary Review Exercises Chapter Test. 5. Similar Triangles. Ratios, Rates and Proportions. Similar Polygons. Proving Triangles Similar. The Pythagorean Theory. Special Right Triangles. Segments Divided Proportionally. PERSPECTIVE ON HISTORY: Ceva's Proof. PERSPECTIVE ON APPLICATION: An Unusual Application of Similar Triangles. Summary Review Exercises Chapter Test. 6. Circles. Circles and Related Segments and Angles. More Angle Measures in the Circle. Line and Segment Relationships in the Circle. 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. 7. Locus and Concurrence. Locus of Points. Concurrence of Lines. More About Regular Polygons. PERSPECTIVE ON HISTORY: The Value of p (Pi). PERSPECTIVE ON APPLICATION: The Nine-Point Circle. Summary Review Exercises Chapter Test. 8. Areas of Polygons and Circles. Areas and Initial Postulates. Perimeter and Area of Polygons. Regular Polygons and Area. Circumference and Area of a Circle. 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. 9. Surfaces and Solids. Prisms, Area, and Volume. Pyramids, Area, and Volume. Cylinders and Cones. Polyhedrons and Spheres. PERSPECTIVE ON HISTORY: Sketch of Rene Descartes. PERSPECTIVE ON APPLICATION: Birds in Flight. Summary Review Exercises Chapter Test. 10. Analytical Geometry. The Rectangular Coordinate System. Graphs of Linear Equations and Slope. Preparing to do Analytic Proofs. Analytic Proofs. Equations of Lines. 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. 11. Introduction to Trigonometry. The Sine Ratio and Applications. The Cosine Ratio and Applications. The Tangent Ratio and Other Ratios. Applications with Acute Triangles. PERSPECTIVE ON HISTORY: Sketch of Plato. PERSPECTIVE ON APPLICATION: Radian Measure of Angles. Summary Review Exercises Chapter Test. Appendix A: Algebra Review. Appendix B: Summaries of Constructions, Postulates, Theorems, and Corollaries Answers. Glossary. Index.