Geometry, 1st edition

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

Photo Credits