Geometry, 2nd edition

Published by Pearson (28 August 2026) © 2027

  • Elayn Martin-Gay University of New Orleans, Lakefront
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Title overview

Elayn Martin-Gay's math program is motivated by her firm belief that every student can succeed. Focus on the student shapes her clear, accessible writing, her effective learning aids, and her popular video resources. Geometry embodies this approach, providing a solid foundation in Euclidean geometry for students who might not have previous experience in the subject.

The 2nd Edition features thoughtful enhancements throughout, including new notes to students, expanded exercises, and a new review feature designed to help students synthesize what they’ve learned. It also emphasizes effective study skills throughout the text and includes carefully refined exercises and explanations to support understanding.

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
  • Mid-Chapter Review: Points, Lines, and Angles
  • 1.6 Angle Pairs and Their Relationships
  • 1.7 Coordinate Geometry–Midpoint and Distance Formulas
  • 1.8 Constructions: Basic Geometry Constructions
  • Review
  • Chapter Test
  • Standardized Test

2. Introduction to Reasoning and Proofs

  • 2.1 Perimeter, Circumference, and Area
  • 2.2 Patterns and Inductive Reasoning
  • 2.3 Conditional Statements
  • Mid-Chapter Review: Perimeter, Area, and 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
  • Vocabulary Check
  • Review
  • Chapter Test
  • Standardized Test

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
  • Mid-Chapter Review: Parallel and Perpendicular Lines and Theorems
  • 3.5 Constructions–Parallel and Perpendicular Lines
  • 3.6 Coordinate Geometry: The Slope of a Line
  • 3.7 Coordinate Geometry: Equations of Lines
  • Vocabulary Check
  • Review
  • Chapter Test
  • Standardized Test

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
  • Mid-Chapter Review: Types of Triangles and Congruent Triangles
  • 4.5 Proofs Using Congruent Triangles
  • 4.6 Isosceles, Equilateral, and Right Triangles
  • Vocabulary Check
  • Review
  • Chapter Test
  • Standardized Test

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
  • Mid-Chapter Review: Bisectors, 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
  • Vocabulary Check
  • Review
  • Chapter Test
  • Standardized Test

6. Quadrilaterals

  • 6.1 Polygons
  • 6.2 Parallelograms
  • 6.3 Proving that a Quadrilateral Is a Parallelogram
  • Mid-Chapter Review: Quadrilaterals and Parallelograms
  • 6.4 Rhombuses, Rectangles, and Squares
  • 6.5 Trapezoids and Kites
  • Vocabulary Check
  • Review
  • Chapter Test
  • Standardized Test

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
  • Mid-Chapter Review:Ratio, Proportion, and Similar Polygons
  • Vocabulary Check
  • Review
  • Chapter Test
  • Standardized Test

8. Transformations

  • 8.1 Rigid Transformations
  • 8.2 Translations
  • 8.3 Reflections
  • Mid-Chapter Review: Translations and Reflections
  • 8.4 Rotations
  • 8.5 Dilations
  • 8.6 Compositions of Reflections
  • Extension: Frieze Patterns
  • Vocabulary Check
  • Review
  • Chapter Test
  • Standardized Test

9. Right Triangles and Trigonometry

  • 9.1 The Pythagorean Theorem and Its Converse
  • 9.2 Special Right Triangles
  • 9.3 Trigonometric Ratios
  • Mid-Chapter Review: Pythagorean Theorem and Trigonometric Ratios
  • 9.4 Solving Right Triangles
  • 9.5 Vectors
  • Extension: Law of Sines
  • Extension: Law of Cosines
  • Vocabulary Check
  • Review
  • Chapter Test
  • Standardized Test

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
  • Mid-Chapter Review: Areas of 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
  • Vocabulary Check
  • Review
  • Chapter Test
  • Standardized Test

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
  • Mid-Chapter Review: Solids and Surface Area
  • 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
  • Vocabulary Check
  • Review
  • Chapter Test
  • Standardized Test

12. Circles and Other Conic Sections

  • 12.1 Circle Review and Tangent Lines
  • 12.2 Chords and Arcs
  • 12.3 Inscribed Angles
  • Mid-Chapter Review: Circles, Tangents, Arcs, and Angles
  • 12.4 Additional Angle Measures and Segment Lengths
  • 12.5 Coordinate Plane: Circles
  • 12.6 Locus
  • Extension: Parabolas
  • Vocabulary Check
  • Review
  • Chapter Test
  • Standardized Test

Appendices

  • A. Review of Basic Concepts
  • B. Tables
  • C. Postulates, Theorems, and Additional Proofs
  • D. Additional Constructions with Circles About Regular Polygons
  • E. Additional Lessons

Answers to Selected Exercises

Subject Index

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