Geometry Companion
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Geometry Companion
This complete online Geometry Companion is fun and easy to use for students already taking a Geometry class. Thinkwell's comprehensive, award-winning video lessons are the heart of the course. After watching a geometry video, your students will review and practice with automatically graded exercises, which give you an instant way to assess their progress. Printable geometry worksheets with answer keys reinforce their learning. Dynamic interactivities allow students to put their newly acquired skills to use.
For a turnkey homeschool course, see www.thinkwellhomeschool.com.
Geometry Companion Course Details:
- Aligned to Geometry National Math Standards
- More than 100 topics with 400+ engaging video lessons
- 34-week lesson plan with daily assignments
- 100+ available contact hours
- 1300+ automatically graded exercises allow you to track your progress
- 24 animated interactivities with audio
- Printable geometry worksheets and answer keys for each subchapter and topic
- Geometry tests, including 13 chapter tests, as well as practice tests, a midterm, and a final exam
- Printable illustrated notes for each topic
- Real-world application examples in both lectures and exercises
- Closed captioning for all video lessons
- Glossary of more than 250 mathematical terms
- Review of essential algebra concepts and applications
- 12-month Online Subscription to our complete Geometry course with video lessons, day-by-day lesson plans, automatically graded exercises, and much more.
Table of Contents
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 x^{2} + bx + c
- 13.4.7 Factoring ax^{2} + 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 is an award-winning professor with a passion for teaching mathematics.
Since 2013, Edward Burger has been President of Southwestern University, a top-ranked liberal arts college in Georgetown, Texas. Previously, he was Professor of Mathematics at Williams College. Dr. Burger earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
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.