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Geometry, 1st edition
Published by Pearson (July 14, 2021) © 2016
- Elayn Martin-Gay University of New Orleans, Lakefront
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Geometry gives you a solid foundation in Euclidean geometry, regardless of your previous experience in geometry. Focused on your success, the author is known for a clear, accessible writing style and for providing innovative resources supporting your mastery of the material.
Table of Contents
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Math Symbols
- Formulas
- Measures
- 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
Photo Credits
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