Note: Each chapter concludes with a Summary and Review Exercises | |
Line and Angle Relationships | |
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 A Look Beyond: Historical Sketch of Euclid | |
Parallel Lines | |
The Parallel Postulate and Special Angles | |
Indirect Proof | |
Proving Lines Parallel | |
The Angles of a Triangle | |
Convex Polygons A Look Beyond: Non-Euclidean Geometries | |
Triangles | |
Congruent Triangles | |
Corresponding Parts of Congruent Triangles | |
Isosceles Triangles | |
Basic Constructions Justified | |
Inequalities in a Triangle A Look Beyond: Historical Sketch of Archimedes | |
Quadrilaterals | |
Properties of a Parallelogram | |
The Parallelogram and Kite | |
The Rectangle, Square, and Rhombus | |
The Trapezoid A Look Beyond: Historical Sketch of Thales | |
Similar Triangles | |
Ratios, Rates, and Proportions | |
Similar Triangles and Polygons | |
The Pythagorean Theorem | |
Special Right Triangles | |
Segments Divided Proportionally A Look Beyond: 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 | |
Constructions and Inequalities for the Circle | |
Locus of Points | |
Concurrency of Lines A Look Beyond: History of Pi | |
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 A Look Beyond: Another Look at the Pythagorean Theorem | |
Surfaces and Solids | |
Prisms, Area, and Volume | |
Pyramids, Area, and Volume | |
Cylinders and Cones | |
Polyhedrons and Spheres A Look Beyond: Historical Sketch of Reneacute; Descartes | |
Analytic Geometry | |
The Rectangular Coordinate System | |
Graphs of Linear Equations and Slope | |
Preparing to Do Analytic Proofs | |
Analytic Proofs | |
Equations of Lines A Look Beyond: The Banach-Tarski Paradox | |
Introduction to Trigonometry | |
The Sine Ratio and Applications | |
The Cosine Ratio and Applications | |
The Tangent Ratio and Other Ratios | |
More Trigonometric Relationships A Look Beyond: Radian Measure of Angles | |
Appendix A | |
Appendix B | |
Appendix C | |
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