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| Introduction | |
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| Deductive Reasoning and Proofs | |
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| The language of geometry | |
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| Deductive reasoning | |
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| Theorems and how to write a proof | |
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| Key axioms and postulates | |
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| Chapter 1 summary and highlights | |
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| Points, Lines, Planes, and Angles | |
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| Points, lines, and planes | |
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| Line segments and distance | |
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| Parallel lines | |
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| Perpendicular lines | |
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| Distances and bisectors | |
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| Rays and angles | |
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| Chapter 2 summary and highlights | |
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| Ratios and Proportions | |
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| Ratios and proportions | |
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| Proportional segments | |
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| Chapter 3 summary and highlights | |
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| Triangles, Congruence, and Similarity | |
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| Triangle definitions, interior angle sum, and exterior angles | |
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| Types of triangles | |
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| Parts of triangles, altitude, bisector, median, and Ceva's Theorem | |
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| Inequalities and triangles | |
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| Congruent triangles | |
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| Similar triangles: Congruent angles and sides in proportion | |
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| Similar right triangles | |
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| Right triangles: Pythagorean Theorem and 30[degree]:60[degree]:90[degree] and 45[degree]:45[degree]:90[degree] triangles | |
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| Triangles and trigonometric functions | |
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| Area of a triangle | |
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| Chapter 4 summary and highlights | |
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| Polygons and Quadrilaterals | |
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| Polygons | |
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| Sum of the interior and exterior angles in a polygon | |
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| Regular polygons and their interior and exterior angle measures | |
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| Quadrilaterals | |
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| Parallelograms | |
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| Special parallelograms: Rectangles, rhombuses, and squares | |
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| Trapezoids | |
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| Area and perimeter of squares, rectangles, parallelograms, rhombuses, trapezoids, other polygons, and regular polygons | |
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| Congruence, area, and similarity | |
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| Chapter 5 summary and highlights | |
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| Circles | |
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| Gircles: Definitions | |
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| Arcs, central angles, and inscribed angles | |
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| Chords, arcs, and angles | |
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| Secants, angles, arcs, and segments | |
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| Tangents | |
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| Circumference and area of circles and sectors | |
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| Circumscribed and inscribed polygons | |
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| Chapter 6 summary and highlights | |
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| Geometric Solids: Surface Area and Volume of Three-Dimensional Objects | |
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| Solids | |
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| Prisms: Cubes, rectangular solids, and oblique and right prisms | |
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| Pyramids | |
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| Cylinders | |
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| Cones | |
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| Spheres | |
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| Similar solids | |
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| Cavalieri's principle | |
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| Chapter 7 summary and highlights | |
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| Constructions and Loci | |
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| Introduction | |
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| Constructions involving lines and angles | |
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| Constructions involving triangles | |
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| Constructions involving circles and polygons | |
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| Construction involving area | |
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| Locus of points | |
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| Chapter 8 summary and highlights | |
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| Coordinate or Analytic Geometry | |
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| Rectangular coordinate systems: Definitions | |
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| Distance between points | |
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| Midpoint formula | |
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| Slope of a line including parallel and perpendicular lines | |
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| Defining linear equations | |
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| Graphing linear equations | |
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| Chapter 9 summary and highlights | |
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| Index | |