Geometry Companion

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 Thinkwell's Geometry Companion package includes: 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 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 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.