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.

- 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