
Elementary Geometry For College Students
by Alexander, Daniel C.; Koeberlein, Geralyn M.-
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Summary
Table of Contents
Line and Angle Relationships | |
Sets, Statements, and Reasoning | |
Informal Geometry and Measurement | |
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 | |
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 | |
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 | |
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 | |
Similar Triangles | |
Ratios, Rates, and Proportions | |
Similar Polygons | |
Proving Triangles Similar | |
The Pythagorean Theorem | |
Special Right Triangles | |
Segments Divided Proportionally | |
Perspective on History: Ceva's Theorem | |
Perspective on Application: An Unusual Application of Similar Triangles | |
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 | |
Perspective on History: Circumference of the Earth | |
Perspective on Application: Sum of the Interior Angles of a Polygon | |
Locus and Concurrence | |
Locus of Points | |
Concurrence of Lines | |
More About Regular Polygons | |
Perspective on History: The Value of Perspective on Application: The Nine-Point Circle | |
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 | |
Perspective on History: Sketch of Pythagoras | |
Perspective on Application: Another Look at the Pythagorean Theorem | |
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 | |
Analytic Geometry | |
The Rectangular Coordinate System | |
Graphs of Linear Equations and Slope | |
Preparing to do Analytic Proofs | |
Analytic Proofs | |
Equations of Lines | |
Perspective on History: The Banach-Tarski Paradox | |
Perspective on Application: The Point-of-Division Formulas | |
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 | |
Appendices | |
Algebra review | |
Summary of Constructions, Postulates, and Theorems and Corollaries | |
Table of Contents provided by Publisher. All Rights Reserved. |
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