Geometry, 1st edition

  • Elayn Martin-Gay

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Overview

Geometry gives you a solid foundation in Euclidean geometry, regardless of your previous experience in geometry. Focused on your success, the author is known for a clear, accessible writing style and for providing innovative resources supporting your mastery of the material.

Published by Pearson (July 14th 2021) - Copyright © 2016

ISBN-13: 9780137554850

Subject: Geometry

Category: Introductory Geometry

Table of contents

Table of Contents

  1. A Beginning of Geometry
    • 1.1 Tips for Success in Mathematics
    • 1.2 Geometry–A Mathematical System
    • 1.3 Points, Lines, and Planes
    • 1.4 Segments and Their Measure
    • 1.5 Angles and Their Measure
    • 1.6 Angle Pairs and Their Relationships
    • 1.7 Coordinate Geometry–Midpoint and Distance Formulas
    • 1.8 Constructions–Basic Geometry Constructions
  2. Introduction to Reasoning and Proofs
    • 2.1 Perimeter, Circumference, and Area
    • 2.2 Patterns and Inductive Reasoning
    • 2.3 Conditional Statements
    • 2.4 Biconditional Statements and Definitions
    • 2.5 Deductive Reasoning
    • 2.6 Reviewing Properties of Equality and Writing Two-Column Proofs
    • 2.7 Proving Theorems About Angles
  3. Parallel and Perpendicular Lines
    • 3.1 Lines and Angles
    • 3.2 Proving Lines Are Parallel
    • 3.3 Parallel Lines and Angles Formed by Transversals
    • 3.4 Proving Theorems About Parallel and Perpendicular Lines
    • 3.5 Constructions–Parallel and Perpendicular Lines
    • 3.6 Coordinate Geometry–The Slope of a Line
    • 3.7 Coordinate Geometry–Equations of Lines
  4. Triangles and Congruence
    • 4.1 Types of Triangles
    • 4.2 Congruent Figures
    • 4.3 Congruent Triangles by SSS and SAS
    • 4.4 Congruent Triangles by ASA and AAS
    • 4.5 Proofs Using Congruent Triangles
    • 4.6 Isosceles, Equilateral, and Right Triangles
  5. Special Properties of Triangles
    • 5.1 Perpendicular and Angle Bisectors
    • 5.2 Bisectors of a Triangle
    • 5.3 Medians and Altitudes of a Triangle
    • 5.4 Midsegments of Triangles
    • 5.5 Indirect Proofs and Inequalities in One Triangle
    • 5.6 Inequalities in Two Triangles
  6. Quadrilaterals
    • 6.1 Polygons
    • 6.2 Parallelograms
    • 6.3 Proving that a Quadrilateral Is a Parallelogram
    • 6.4 Rhombuses, Rectangles, and Squares
    • 6.5 Trapezoids and Kites
  7. Similarity
    • 7.1 Ratios and Proportions
    • 7.2 Proportion Properties and Problem Solving
    • 7.3 Similar Polygons
    • 7.4 Proving Triangles Are Similar
    • 7.5 Geometric Mean and Similarity in Right Triangles
    • 7.6 Additional Proportions in Triangles
  8. Transformations
    • 8.1 Rigid Transformations
    • 8.2 Translations
    • 8.3 Reflections
    • 8.4 Rotations
    • 8.5 Dilations
    • 8.6 Compositions of Reflections
    • Extension–Frieze Patterns
  9. Right Triangles and Trigonometry
    • 9.1 The Pythagorean Theorem and Its Converse
    • 9.2 Special Right Triangles
    • 9.3 Trigonometric Ratios
    • 9.4 Solving Right Triangles
    • 9.5 Vectors
    • Extension–Law of Sines
    • Extension–Law of Cosines
  10. Area
    • 10.1 Angle Measures of Polygons and Regular Polygon Tessellations
    • 10.2 Areas of Triangles and Quadrilaterals with a Review of Perimeter
    • 10.3 Areas of Regular Polygons
    • 10.4 Perimeters and Areas of Similar Figures
    • 10.5 Arc Measures, Circumferences, and Arc Lengths of Circles
    • 10.6 Areas of Circles and Sectors
    • 10.7 Geometric Probability
  11. Surface Area and Volume
    • 11.1 Solids and Cross Sections
    • 11.2 Surface Areas of Prisms and Cylinders
    • 11.3 Surface Areas of Pyramids and Cones
    • 11.4 Volumes of Prisms and Cylinders and Cavalieri’s Principle
    • 11.5 Volumes of Pyramids and Cones
    • 11.6 Surface Areas and Volumes of Spheres
    • 11.7 Areas and Volumes of Similar Solids
  12. Circles and Other Conic Sections
    • 12.1 Circle Review and Tangent Lines
    • 12.2 Chords and Arcs
    • 12.3 Inscribed Angles
    • 12.4 Additional Angle Measures and Segment Lengths
    • 12.5 Coordinate Plane–Circles
    • 12.6 Locus
    • Extension–Parabolas

Student Success Resource Section

A Review of Basic Concepts

  • A.1 Measurement Conversions
  • A.2 Probability
  • A.3 Exponents, Order of Operations, and Variable Expressions
  • A.4 Operations on Real Numbers
  • A.5 Simplifying Expressions
  • A.6 Solving Linear Equations
  • A.7 Solving Linear Inequalities
  • A.8 Solving Formulas for a Variable
  • A.9 The Coordinate Plane
  • A.10 Graphing Linear Equations
  • A.11 Solving Systems of Linear Equations in Two Variables
  • A.12 Exponents
  • A.13 Multiplying Polynomials
  • A.14 Simplifying Radical Expressions
  • A.15 Solving Quadratic Equations by Factoring
  • A.16 Solving Quadratic Equations by the Square Root Property
  • A.17 Solving Quadratic Equations by the Quadratic Formula

Tables

  1. Math Symbols
  2. Formulas
  3. Measures
  4. Properties of Real Numbers Postulates, Theorems, and Additional Proofs

B. Additional Lessons

  • B.1 Ellipses and Hyperbolas
  • B.2 Measurement, Rounding Error, and Reasonableness
  • B.3 The Effect of Measurement Errors on Calculations

Answers to Selected Exercises

Index

Photo Credits

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