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Geometry, 1st edition

  • Elayn Martin-Gay

Published by Pearson (June 4th 2015) - Copyright © 2016

1st edition

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Every student can succeed

Elayn Martin-Gay's developmental math program is motivated by her firm belief that every student can succeed. Martin-Gay's focus on the student shapes her clear, accessible writing, inspires her constant pedagogical innovations, and contributes to the popularity and effectiveness of her video resources. Geometry continues her focus on students and what they need to be successful. It was written to provide a solid foundation in Euclidean geometry for students who may not have previous experience in geometry.


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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



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



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


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