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Geometry Details
Thinkwell's Geometry with Edward Burger lays the foundation for success because, unlike a traditional textbook, students actually like using it. Thinkwell works with the learning styles of students who have found that traditional textbooks are not effective. Watch one Thinkwell video lecture and you'll understand why Thinkwell works better.
Comprehensive Video Tutorials
We've built Geometry around hundreds of multimedia tutorials that provide dozens of hours of instructional material. Thinkwell offers a more engaging, more effective way for you to learn.
Instead of reading dense chunks of text from a printed book, you can watch video lectures filled with illustrations, examples, and even humor. Students report learning more easily with Thinkwell than with traditional textbooks.
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There are hundreds of exercise items with fully worked-out solutions and explanations. Each video topic has corresponding exercises to test your understanding.
Test your understanding with hundreds of exercises that are automatically graded. Your results are available immediately, including fully worked-out solutions and explanations for each exercise. You can work on the exercises at the computer or print them out to work on later. Access your cumulative results anytime.
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While the video lectures are the heart of Thinkwell products, we also offer concise, illustrated review notes, a glossary, transcripts of the video lectures, and links to relevant websites. All of these materials may be viewed online, and the notes and transcripts may be printed and kept for reference.
Table of Contents
(Expand All - Close All)1. Fundamentals of Geometry
- 1.1 Points, Lines, Planes, and Angles
- 1.1.1 Understanding Points, Lines, and Planes
- 1.1.2 Measuring and Constructing Segments
- 1.1.3 Measuring and Constructing Angles
- 1.1.4 Pairs of Angles
- 1.2 Coordinate and Transformation Tools
- 1.2.1 Using Formulas in Geometry
- 1.2.2 Midpoint and Distance in the Coordinate Plane
- 1.2.3 Transformations in the Coordinate Plane
2. Reasoning and Writing Geometric Proofs
- 2.1 Inductive and Deductive Reasoning
- 2.1.1 Using Inductive Reasoning to Make Conjectures
- 2.1.2 Conditional Statements
- 2.1.3 Using Deductive Reasoning to Verify Conjectures
- 2.1.4 Biconditional Statements and Definitions
- 2.2 Mathematical Proof
- 2.2.1 Algebraic Proof
- 2.2.2 Geometric Proof
- 2.2.3 Flowchart and Paragraph Proofs
3. Parallel and Perpendicular Lines
- 3.1 Lines with Transversals
- 3.1.1 Planes, Lines, and Angles
- 3.1.2 Angles, Parallel Lines, and Transversals
- 3.1.3 Proving that Lines are Parallel
- 3.1.4 Properties of Perpendicular Lines
- 3.2 Slope and the Equation of a Line
- 3.2.1 Finding the Slope Given Two Points
- 3.2.2 Slope-Intercept Form
- 3.2.3 Point-Slope Form
- 3.2.4 Slopes of Parallel and Perpendicular Lines
4. Triangle Congruence
- 4.1 Triangles and Congruence
- 4.1.1 Classifying Triangles
- 4.1.2 Angle Relationships in Triangles
- 4.1.3 Congruent Triangles
- 4.2 Proving Triangle Congruence
- 4.2.1 Triangle Congruence: SSS and SAS
- 4.2.2 Triangle Congruence: ASA, AAS, and HL
- 4.2.3 Triangle Congruence: CPCTC
- 4.2.4 Introduction to Coordinate Proof
- 4.2.5 Isosceles and Equilateral Triangles
5. Properties and Attributes of Triangles
- 5.1 Segments in Triangles
- 5.1.1 Perpendicular and Angle Bisector Theorems
- 5.1.2 Medians, Altitudes, and Midsegments in Triangles
- 5.2 Relationships in Triangles
- 5.2.1 Indirect Proof and Inequalities in One Triangle
- 5.2.2 Inequalities in Two Triangles
- 5.2.3 The Pythagorean Theorem
- 5.2.4 Applying Special Right Triangles
6. Polygons and Quadrilaterals
- 6.1 Polygons and Parallelograms
- 6.1.1 Properties and Attributes of Polygons
- 6.1.2 Properties of Parallelograms
- 6.1.3 Conditions for Parallelograms
- 6.2 Other Special Quadrilaterals
- 6.2.1 Properties of Special Parallelograms
- 6.2.2 Conditions for Special Parallelograms
- 6.2.3 Properties of Kites and Trapezoids
7. Similarity
- 7.1 Similarity Relationships
- 7.1.1 Ratio and Proportion
- 7.1.2 Ratios in Similar Polygons
- 7.1.3 Triangle Similarity: AA, SSS, and SAS
- 7.2 Applying Similarity
- 7.2.1 Applying Properties of Similar Triangles
- 7.2.2 Using Proportional Relationships
- 7.2.3 Dilations and Similarity in the Coordinate Plane
8. Right Triangles and Trigonometry
- 8.1 Trigonometric Ratios
- 8.1.1 Similarity in Right Triangles
- 8.1.2 Trigonometric Ratios
- 8.1.3 Solving Right Triangles
- 8.2 Applying Trigonometric Ratios
- 8.2.1 Angles of Elevation and Depression
- 8.2.2 Law of Sines and Law of Cosines
- 8.2.3 Vectors
9. Extending Perimeter, Circumference, and Area
- 9.1 Developing Geometric Formulas
- 9.1.1 Developing Formulas for Triangles and Quadrilaterals
- 9.1.2 Developing Formulas for Circles and Regular Polygons
- 9.1.3 Composite Figures
- 9.2 Applying Geometric Formulas
- 9.2.1 Perimeter and Area in the Coordinate Plane
- 9.2.2 Effects of Changing Dimensions Proportionally
- 9.2.3 Geometric Probability
10. Spatial Reasoning
- 10.1 Three-Dimensional Figures
- 10.1.1 Solid Geometry
- 10.1.2 Representations of Three-Dimensional Figures
- 10.1.3 Formulas in Three Dimensions
- 10.2 Surface Area and Volume
- 10.2.1 Surface Area of Prisms and Cylinders
- 10.2.2 Surface Area of Pyramids and Cones
- 10.2.3 Volume of Prisms and Cylinders
- 10.2.4 Volume of Pyramids and Cones
- 10.2.5 Spheres
11. Circles
- 11.1 Lines and Arcs in Circles
- 11.1.1 Lines That Intersect Circles
- 11.1.2 Arcs and Chords
- 11.1.3 Sector Area and Arc Length
- 11.2 Angles and Segments in Circles
- 11.2.1 Inscribed Angles
- 11.2.2 Angle Relationships in Circles
- 11.2.3 Segment Relationships in Circles
- 11.2.4 Circles in the Coordinate Plane
12. Transformational Geometry
- 12.1 Congruence Transformations
- 12.1.1 Reflections
- 12.1.2 Translations
- 12.1.3 Rotations
- 12.1.4 Compositions of Transformations
- 12.2 Patterns
- 12.2.1 Symmetry
- 12.2.2 Tessellations
- 12.2.3 Dilations
13. Appendix: Essential Algebra Review
- 13.1 Solving Equations and Inequalities
- 13.1.1 Simplifying Expressions
- 13.1.2 Writing and Solving Two-Step Equations
- 13.1.3 Solving Two-Step Inequalities
- 13.1.4 Writing and Solving Multi-Step Equations
- 13.1.5 Solving Equations with Variables on Both Sides
- 13.1.6 Systems of Equations
- 13.2 Graphing and the Coordinate Plane
- 13.2.1 The Coordinate Plane
- 13.2.2 Equations, Tables, and Graphs
- 13.2.3 Graphing Using Intercepts
- 13.3 Ratio and Proportion
- 13.3.1 Rates, Ratios, and Proportions
- 13.3.2 Applications of Proportions
- 13.3.3 Finding and Using Percents
- 13.4 Operations with Polynomials and Factoring
- 13.4.1 Adding and Subtracting Polynomials
- 13.4.2 Multiplying and Dividing Monomials
- 13.4.3 Multiplying Monomials by Polynomials
- 13.4.4 Multiplying Binomials
- 13.4.5 Factoring with the GCF
- 13.4.6 Factoring x2 + bx + c
- 13.4.7 Factoring ax2 + bx + c
- 13.5 Radicals and Solving Quadratics
- 13.5.1 Radical Expressions
- 13.5.2 Solving Quadratic Equations by Factoring
- 13.5.3 Solving Quadratic Equations by Using Square Roots
About the Author
Edward Burger
Williams College
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest listed him in the "100 Best of America". After completing his tenure as Gaudino Scholar at Williams, he was named Lissack Professor for Social Responsibility and Personal Ethics.
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.
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