Geometry

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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Elayn Martin-Gay has taught mathematics at the University of New Orleans for more than 25 years. Her numerous teaching awards include the local University Alumni Association’s Award for Excellence in Teaching, and Outstanding Developmental Educator at University of New Orleans, presented by the Louisiana Association of Developmental Educators.

Prior to writing textbooks, Elayn Martin-Gay developed an acclaimed series of lecture videos to support developmental mathematics students. These highly successful videos originally served as the foundation materials for her texts. Today, the videos are specific to each book in her series. She has also created Chapter Test Prep Videos to help students during their most “teachable moment”–as they prepare for a test–along with Instructor-to-Instructor videos that provide teaching tips, hints, and suggestions for every developmental mathematics course, including basic mathematics, prealgebra, beginning algebra, and intermediate algebra.

Elayn is the author of 12 published textbooks and numerous multimedia interactive products, all specializing in developmental mathematics courses. She has also published series in Algebra 1, Algebra 2, and Geometry.  She has participated as an author across a broad range of educational materials: textbooks, videos, tutorial software, and courseware. This offers an opportunity for multiple combinations for an integrated teaching and learning package, offering great consistency for the student.

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

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