Easy Way Series: E-Z Geometry

Editor/Author Leff, Lawrence S.
Publication Year: 2009
Publisher: Barron's Educational Series

Price: Core Collection Only
ISBN: 978-0-76-413918-5
Category: Mathematics & Statistics - Mathematics
Image Count: 680
Book Status: Available
Table of Contents

E-Z Geometry covers the "how" and "why" of geometry, with examples, exercises, and solutions throughout, plus hundreds of drawings, graphs, and tables.

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Table of Contents

  • Preface
  • 1 Building a Geometry Vocabulary
  • The Building Blocks of Geometry
  • Definitions and Postulates
  • Inductive Versus Deductive Reasoning
  • The IF ... THEN ... Sentence Structure
  • Review Exercises for Chapter 1
  • 2 Measure and Congruence
  • Measuring Segments and Angles
  • Betweenness of Points and Rays
  • Congruence
  • Midpoint and Bisector
  • Diagrams and Drawing Conclusions
  • Properties of Equality and Congruence
  • Additional Properties of Equality
  • The Two-Column Proof Format
  • Review Exercises for Chapter 2
  • 3 Angle Pairs and Perpendicular Lines
  • Supplementary and Complementary Angle Pairs
  • Adjacent and Vertical Angle Pairs
  • Theorems Relating to Complementary, Supplementary, and Vertical Angles
  • Definitions and Theorems Relating to Right Angles and Perpendiculars
  • A Word About the Format of a Proof
  • Review Exercises for Chapter 3
  • 4 Parallel Lines
  • Planes and Lines
  • Properties of Parallel Lines
  • Converses and Methods of Proving Lines Parallel
  • The Parallel Postulate
  • Review Exercises for Chapter 4
  • 5 Angles of a Polygon
  • The Anatomy of a Polygon
  • Angles of a Triangle
  • Exterior Angles of a Triangle
  • Angles of a Polygon
  • Review Exercises for Chapter 5
  • 6 Proving Triangles Are Congruent
  • Correspondences and Congruent Triangles
  • Proving Triangles Congruent: SSS, SAS, and ASA Postulates
  • Proving Overlapping Triangles Congruent
  • Proving Triangles Congruent: AAS and Hy-Leg Methods
  • When Two Triangles Are NOT Congruent
  • Review Exercises for Chapter 6
  • 7 Applying Congruent Triangles
  • Using Congruent Triangles to Prove Segments and Angles Congruent
  • Using Congruent Triangles to Prove Special Properties of Lines
  • Classifying Triangles and Special Segments
  • The Isosceles Triangle
  • Double Congruence Proofs
  • Review Exercises for Chapter 7
  • Cumulative Review Exercises: Chapters 1-7
  • 8 Geometric Inequalities
  • Some Basic Properties of Inequalities
  • Inequality Relationships in a Triangle
  • The Indirect Method of Proof
  • Review Exercises for Chapter 8
  • 9 Special Quadrilaterals
  • Classifying Quadrilaterals
  • Properties of a Parallelogram
  • Properties of Special Parallelograms
  • Proving a Quadrilateral Is a Parallelogram
  • Applications of Parallelograms
  • Properties of a Trapezoid
  • Review Exercises for Chapter 9
  • 10 Ratio, Proportion, and Similarity
  • Ratio and Proportion
  • Proportions in a Triangle
  • When Are Polygons Similar?
  • Proving Triangles Similar
  • Proving Lengths of Sides of Similar Triangles in Proportion
  • Proving Products of Segment Lengths Equal
  • Review Exercises for Chapter 10
  • 11 The Right Triangle
  • Proportions in a Right Triangle
  • The Pythagorean Theorem
  • Special Right-Triangle Relationships
  • Trigonometric Ratios
  • Indirect Measurement in a Right Triangle
  • Review Exercises for Chapter 11
  • Cumulative Review Exercises: Chapters 8-11
  • 12 Circles and Angle Measurement
  • The Parts of a Circle
  • Arcs and Central Angles
  • Diameters and Chords
  • Tangents and Secants
  • Angle Measurement: Vertex on the Circle
  • Angle Measurement: Vertex in the Interior of the Circle
  • Angle Measurement: Vertex in the Exterior of the Circle
  • Using Angle-Measurement Theorems
  • Review Exercises for Chapter 12
  • 13 Chord, Tangent, and Secant Segments
  • Equidistant Chords
  • Tangents and Circles
  • Similar Triangles and Circles
  • Tangent- and Secant-Segment Relationships
  • Circumference and Arc Length
  • Review Exercises for Chapter 13
  • 14 Area and Volume
  • Areas of a Rectangle, Square, and Parallelogram
  • Areas of a Triangle and Trapezoid
  • Comparing Areas
  • Area of a Regular Polygon
  • Areas of a Circle, Sector, and Segment
  • Geometric Solids
  • Review Exercises for Chapter 14
  • 15 Coordinate Geometry
  • The Coordinate Plane
  • Finding Area Using Coordinates
  • The Midpoint and Distance Formulas
  • Slope of a Line
  • Equation of a Line
  • Equation of a Circle
  • Proofs Using Coordinates
  • Review Exercises for Chapter 15
  • 16 Locus and Constructions
  • Describing Points That Fit One Condition
  • Describing Points That Fit More Than One Condition
  • Locus and Coordinates
  • Basic Constructions
  • Review Exercises for Chapter 16
  • 17 Transformation Geometry
  • Terms and Notation
  • Congruence Transformations
  • Classifying Isometries
  • Size Transformations
  • Types of Symmetry
  • Transformations in the Coordinate Plane
  • Composing Transformations
  • Review Exercises for Chapter 17
  • Cumulative Review Exercises: Chapters 12-17
  • Some Geometric Relationships and Formulas Worth Remembering
  • Glossary
  • Answers to Chapter Exercises
  • Solutions to Cumulative Review Exercises