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Line and Angle Relationships | |
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Sets, Statements, and Reasoning | |
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Informal Geometry and Measurement | |
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Early Definitions and Postulates | |
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Angles and Their Relationships | |
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Introduction to Geometric Proof | |
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Relationships: Perpendicular Lines | |
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The Formal Proof of a Theorem | |
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Perspective on History: The Development of Geometry | |
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Perspective on Application: Patterns | |
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Parallel Lines | |
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The Parallel Postulate and Special Angles | |
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Indirect Proof | |
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Proving Lines Parallel | |
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The Angles of a Triangle | |
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Convex Polygons | |
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Symmetry and Transformations | |
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Perspective on History: Sketch of Euclid | |
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Perspective on Application: Non-Euclidean Geometries | |
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Triangles | |
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Congruent Triangles | |
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Corresponding Parts of Congruent Triangles | |
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Isosceles Triangles | |
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Basic Constructions Justified | |
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Inequalities in a Triangle | |
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Perspective on History: Sketch of Archimedes | |
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Perspective on Application: Pascal's Triangle | |
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Quadrilaterals | |
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Properties of a Parallelogram | |
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The Parallelogram and Kite | |
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The Rectangle, Square, and Rhombus | |
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The Trapezoid | |
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Perspective on History: Sketch of Thales | |
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Perspective on Application: Square Numbers as Sums | |
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Similar Triangles | |
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Ratios, Rates, and Proportions | |
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Similar Polygons | |
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Proving Triangles Similar | |
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The Pythagorean Theorem | |
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Special Right Triangles | |
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Segments Divided Proportionally | |
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Perspective on History: Ceva's Theorem | |
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Perspective on Application: An Unusual Application of Similar Triangles | |
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Circles | |
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Circles and Related Segments and Angles | |
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More Angle Measures in the Circle | |
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Line and Segment Relationships in the Circle | |
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Some Constructions and Inequalities for the Circle | |
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Perspective on History: Circumference of the Earth | |
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Perspective on Application: Sum of the Interior Angles of a Polygon | |
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Locus and Concurrence | |
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Locus of Points | |
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Concurrence of Lines | |
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More About Regular Polygons | |
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Perspective on History: The Value of Perspective on Application: The Nine-Point Circle | |
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Areas of Polygons and Circles | |
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Area and Initial Postulates | |
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Perimeter and Area of Polygons | |
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Regular Polygons and Area | |
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Circumference and Area of a Circle | |
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More Area Relationships in the Circle | |
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Perspective on History: Sketch of Pythagoras | |
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Perspective on Application: Another Look at the Pythagorean Theorem | |
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Surfaces and Solids | |
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Prisms, Area, and Volume | |
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Pyramids, Area, and Volume | |
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Cylinders and Cones | |
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Polyhedrons and Spheres | |
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Perspective on History: Sketch of Rene Descartes | |
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Perspective on Application: Birds in Flight | |
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Analytic Geometry | |
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The Rectangular Coordinate System | |
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Graphs of Linear Equations and Slope | |
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Preparing to do Analytic Proofs | |
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Analytic Proofs | |
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Equations of Lines | |
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Perspective on History: The Banach-Tarski Paradox | |
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Perspective on Application: The Point-of-Division Formulas | |
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Introduction to Trigonometry | |
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The Sine Ratio and Applications | |
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The Cosine Ratio and Applications | |
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The Tangent Ratio and Other Ratios | |
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Applications with Acute Triangles. | |
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Perspective on History: Sketch of Plato | |
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Perspective on Application: Radian Measure of Angles | |
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Appendices | |
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Algebra review | |
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Summary of Constructions, Postulates, and Theorems and Corollaries | |