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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 | |