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Master Math: Geometry was written for students, teachers, tutors, and parents, as well as for scientists and engineers who need to look up principles, definitions, explanations of concepts, and pertinent examples. It provides everything a high school or first year college student needs to know about Geometry including: explanation of deductive reasoning, how to perform proofs, definitions, theorems, and postulates. It includes explanations of deductive reasoning, examples pertaining to points, lines, plans, angles, and ratios, coverage on triangles, quadrilaterals, polygons, and much more!

Tabla de contenidos provista por Syndetics

• Introduction(p. 1)
• Chapter 1 Deductive Reasoning and Proofs(p. 3)
• 1.1 The language of geometry(p. 3)
• 1.2 Deductive reasoning(p. 7)
• 1.3 Theorems and how to write a proof(p. 10)
• 1.4 Key axioms and postulates(p. 15)
• 1.5 Chapter 1 summary and highlights(p. 22)
• Chapter 2 Points, Lines, Planes, and Angles(p. 24)
• 2.1 Points, lines, and planes(p. 24)
• 2.2 Line segments and distance(p. 28)
• 2.3 Parallel lines(p. 34)
• 2.4 Perpendicular lines(p. 40)
• 2.5 Distances and bisectors(p. 41)
• 2.6 Rays and angles(p. 46)
• 2.7 Chapter 2 summary and highlights(p. 60)
• Chapter 3 Ratios and Proportions(p. 62)
• 3.1 Ratios and proportions(p. 63)
• 3.2 Proportional segments(p. 73)
• 3.3 Chapter 3 summary and highlights(p. 81)
• Chapter 4 Triangles, Congruence, and Similarity(p. 82)
• 4.1 Triangle definitions, interior angle sum, and exterior angles(p. 82)
• 4.2 Types of triangles(p. 91)
• 4.3 Parts of triangles, altitude, bisector, median, and Ceva's Theorem(p. 97)
• 4.4 Inequalities and triangles(p. 110)
• 4.5 Congruent triangles(p. 115)
• 4.6 Similar triangles: Congruent angles and sides in proportion(p. 127)
• 4.7 Similar right triangles(p. 143)
• 4.8 Right triangles: Pythagorean Theorem and 30[degree]:60[degree]:90[degree] and 45[degree]:45[degree]:90[degree] triangles(p. 148)
• 4.9 Triangles and trigonometric functions(p. 163)
• 4.10 Area of a triangle(p. 174)
• 4.11 Chapter 4 summary and highlights(p. 178)
• Chapter 5 Polygons and Quadrilaterals(p. 181)
• 5.1 Polygons(p. 182)
• 5.2 Sum of the interior and exterior angles in a polygon(p. 183)
• 5.3 Regular polygons and their interior and exterior angle measures(p. 187)
• 5.4 Quadrilaterals(p. 193)
• 5.5 Parallelograms(p. 195)
• 5.6 Special parallelograms: Rectangles, rhombuses, and squares(p. 202)
• 5.7 Trapezoids(p. 211)
• 5.8 Area and perimeter of squares, rectangles, parallelograms, rhombuses, trapezoids, other polygons, and regular polygons(p. 215)
• 5.9 Congruence, area, and similarity(p. 232)
• 5.10 Chapter 5 summary and highlights(p. 235)
• Chapter 6 Circles(p. 237)
• 6.1 Gircles: Definitions(p. 239)
• 6.2 Arcs, central angles, and inscribed angles(p. 242)
• 6.3 Chords, arcs, and angles(p. 253)
• 6.4 Secants, angles, arcs, and segments(p. 260)
• 6.5 Tangents(p. 264)
• 6.6 Circumference and area of circles and sectors(p. 267)
• 6.7 Circumscribed and inscribed polygons(p. 274)
• 6.8 Chapter 6 summary and highlights(p. 276)
• Chapter 7 Geometric Solids: Surface Area and Volume of Three-Dimensional Objects(p. 278)
• 7.1 Solids(p. 278)
• 7.2 Prisms: Cubes, rectangular solids, and oblique and right prisms(p. 280)
• 7.3 Pyramids(p. 285)
• 7.4 Cylinders(p. 289)
• 7.5 Cones(p. 291)
• 7.6 Spheres(p. 293)
• 7.7 Similar solids(p. 295)
• 7.8 Cavalieri's principle(p. 297)
• 7.9 Chapter 7 summary and highlights(p. 298)
• Chapter 8 Constructions and Loci(p. 300)
• 8.1 Introduction(p. 300)
• 8.2 Constructions involving lines and angles(p. 302)
• 8.3 Constructions involving triangles(p. 312)
• 8.4 Constructions involving circles and polygons(p. 318)
• 8.5 Construction involving area(p. 329)
• 8.6 Locus of points(p. 330)
• 8.7 Chapter 8 summary and highlights(p. 333)
• Chapter 9 Coordinate or Analytic Geometry(p. 334)
• 9.1 Rectangular coordinate systems: Definitions(p. 335)
• 9.2 Distance between points(p. 339)
• 9.3 Midpoint formula(p. 343)
• 9.4 Slope of a line including parallel and perpendicular lines(p. 346)
• 9.5 Defining linear equations(p. 351)
• 9.6 Graphing linear equations(p. 354)
• 9.7 Chapter 9 summary and highlights(p. 357)
• Index(p. 358)

Reseñas proporcionadas por Syndetics

CHOICE Review

Ross provides a solid summary of basic geometric definitions, theorems, and concepts encountered in the secondary school curriculum. Master Math is logically arranged into nine chapters, commencing with deductive reasoning and proofs, continuing with angles, polygons, circles, and three-dimensional solids, and concluding with analytic geometry. Crisply presented diagrams abound and illustrate well the concepts at hand, and two-column proofs of many standard theorems are scattered throughout the book. This work is intended to serve as a resource and includes no additional problem sets. Occasionally, one might like to see alternative terminology introduced (with no reference to "opposite angles" when vertical angles are considered.) Similarly, while Heron's formula is included in the section on areas of triangles, one will not find a reference to it in the index. However, such concerns are minor and rare. The author wasted no time on high-level, obscure results (like the Butterfly Theorem), but instead concentrates on the standard concerns encountered in secondary geometry courses. This reviewer would especially recommend this book to anyone teaching geometry for the first time as a solid resource for those many ideas that might be long-since forgotten. ^BSumming Up: Highly recommended. High school students; general readers; lower-division undergraduates. N. W. Schillow Lehigh Carbon Community College

Notas de autor provistas por Syndetics

Debra Anne Ross has a double BA in Chemistry and Biology from the University of California, Santa Cruz, and an MS in Chemical Engineering from Stanford University