(Ebook) Elementary geometry for college students by Alexander, Daniel C.; Koeberlein, Geralyn M ISBN 9781439047903, 1439047901

(Ebook) Elementary geometry for college students by Alexander, Daniel C.; Koeberlein, Geralyn M ISBN 9781439047903, 1439047901

2. Parallel lines -- the parallel postulate and special angles -- Indirect proof -- Proving lines parallel -- The angles of a triangle -- Convex polygons -- Symmetry and transformations -- Sketch of Euclid -- Non-Euclidean geometrics;3. Triangles -- Congruent triangles -- Corresponding parts of congruent triangles -- Isosceles triangles -- Basic constructions justified -- Inequalities in a triangle -- Sketch of Archimedes -- Pascal's triangle;6. Circles -- Circles and related segments and angles -- More angle measures in the circle -- Line and segment relationships in the circle -- Some constructions and inequalities for the circle -- Circumference of the earth -- Sum of the interior angles of a polygon;8. Areas of polygons and circles -- Area and initial postulates -- Perimeter and area of polygons -- Regular polygons and area -- Circumference and area of a circle -- More area relationships in the circle -- Sketch of Pythagoras -- Another look at the Pythagorean theorem;10. Analytic geometry -- The rectangular coordinate system -- Graphs of linear equations and slope -- Preparing to do analytic proofs -- Analytic proofs -- Equations of lines -- The Banach-Tarski paradox -- The point-of-division formulas;4. Quadrilaterals -- Properties of a parallelogram -- The parallelogram and kite -- The rectangle, square, and rhombus -- The trapezoid -- Sketch of Thales -- Square numbers as sums;5. Similar triangles -- Ratios, rates, proportions -- Similar polygons -- Proving triangles similar -- The Pythagorean theorem -- Special right triangles -- Segments divided proportionally -- Ceva's proof -- An unusual application of similar triangles;11. Introduction to trigonometry -- The sine ratio and applications -- The cosine ratio and applications -- The tangent ratio and other ratios -- Applications with acute triangles -- Sketch of Plato -- Radian measure of angles -- Appendix A: Algebra review -- Appendix B: Summary of constructions, postulates, theorems, and corollaries;1. Line and angle relationships -- Sets, statements, and reasoning -- Early definitions and postulates -- Angles and their relationships -- Introduction to geometric proof -- Relationships: perpendicular lines -- The formal proof of a theorem -- The development of geometry -- Patterns;7. Locus and concurrence -- Locus of points -- Concurrence of lines -- More about regular polygons -- The value of pi -- The nine-point circle;9. Surfaces and solids -- Prisms, area, and volume -- Pyramids, area, and volume -- Cylinders and cones -- Polyhedrons and spheres -- Sketch of René Descartes -- Birds in flight