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Geometry
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Currently enrolled students login here
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Description
This course will cover the topics normally covered in a high school geometry course. This course is normally taken by students in grade nine or ten. Students should have completed Algebra 1 before enrolling in Geometry. A detailed course syllabus is shown below.
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Fees
The cost of the course is $78 per month for nine months for students attending the class, $58 per month for distance learners. Registration fees for homeschool classes at various locations (LAC, SNA, Dunwoody, etc) will also apply. Students will need to purchase a copy of the “Student Notes and Workbook”, which should be less than $20. Students may borrow a copy of the textbook from the teacher at no charge, and videos of the class lectures will be provided on computer disc or via the internet at no additional cost.
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Lecture Notes and Class Time
Class time will primarily be spent on instruction. The lecture notes are a key part of the class. These notes are prepared in advance and given to the students, but with much of the material deleted and replaced by blank space on the page. During the lecture, the students fill in the gaps, solve the example problems, and add any notes they need to. By the end of the year, the students will have what amounts to their own complete text made from the lectures delivered and the problems worked in class. A sample of these lecture notes is in the PDF course description and under "Lecture Notes" on the menu of this web site.
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Textbook
Geometry: Seeing, Doing, Understanding by Howard R. Jacobs, 3rd Edition, published by W. H. Freeman, 2003. This is an extremely readable and engaging math textbook. The text emphasis Euclidean geometry and explains the importance of logical reasoning and proof in mathematics. It has numerous practical and interesting examples and shows the many applications of geometry in the real world. It also touches on some important topics in analytic geometry (geometry in the coordinate plane), a topic that is essential for much further study in mathematics. Throughout the book, there are also sections of algebra review so that the students do not lose touch with their algebra skills during their course in Geometry.
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Homework, Tests and Grades
Students will be given specific assignments to do on their own each week. Assignments will consist of additional lectures delivered on the computer, problems to practice, and homework assignments that will be collected and graded. To allow for the maximum amount of instructional time in class, tests will be given at home. One final exam for each semester will be taken in class at the end of the semester. Students will receive a numerical grade for each semester and for the year. The grade is calculated based on tests, graded homework and the final exams.
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Difficulty Level
Not all students require the same pace and difficulty level. Some may need or prefer a class that is more challenging and at a faster pace, while some may desire a class that is not accelerated. This class is offered simultaneously on two difficulty levels, standard and honors. The lectures are the same for both. The honors students will have additional homework that is more difficult, and will have more challenging tests. Note that the honors class is not an AP class. It is simply a more challenging version of the same course. The goal is for the classes to closely correspond to “Standard Geometry" and “Honors Geometry" classes at a good private school. Students will decide whether they would prefer the standard or honors version of the course about a month into the course, after having had a chance to look at some tests and assignments.
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Computer Access
Access to a computer (Windows, Mac, or Linux) with either a CD drive or a high speed internet connection is strongly recommended for this course. Videos of the lectures will be available to the students over the web or on CD. These lectures contain both audio and video and cover the same material covered in class. The videos allow students to review the material, to hear the explanations again if needed, and to see example problems being worked out with detailed explanations. They also insure that the students receive all of the instruction, even if they miss a class or if all of the material is not covered given the limited class time.
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The Instructor
Derek Owens taught physics, honors physics, AP Physics, and AP computer science at The Westminster Schools in Atlanta, GA from 1988-2000. He currently teaches Physics in the summer school program at Westminster as well as AP Calculus as Providence Christian Academy. He graduated from Duke University in 1988 with a degree in mechanical engineering and physics, and worked at the TIP program at Duke for two years, teaching physics and heading the Satellite Science Program. He received a National Science Foundation scholarship and studied history and philosophy of science at L’Abri Fellowship in England. He worked as a software developer for five years before returning to teaching. This will be his sixth school year teaching homeschoolers in the Atlanta area. He and his wife Amor and their two children Claire and David attend Grace Fellowship Church, a non-denominational church near their home in Lawrenceville.
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Course Syllabus
These topics comprise the material normally taught in a high school Geometry course.
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Chapter 1: Basics Ideas of Geometry
Points, Lines, Planes, and Space; Distance and Segment Measure; Rays, Angles and Angle Measure, Congruent Segments and Angles, Triangles; Conditional Statements; Drawing Conclusions; Deductive Reasoning
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Chapter 2: Proof
Two-Column Proofs; Complimentary, Supplementary, and Vertical Angles; Perpendicular Lines; Diagrams; Writing Proofs; Proving Theorems
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Chapter 3: Parallel Lines and Planes
Parallel Planes, Lines, and Transversals; Properties of Parallel Lines; Proving Lines Parallel; Angles of a Triangle; Angle Sum Theorem; Angles of a Polygon
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Chapter 4: Congruent Triangles
Congruent Triangles; Congruence Postulates; Proving Segments and Angles Congruent; Isosceles Triangles; AAS Congruence; Right Triangle Congruence; Medians, Altitudes, and Perpendicular Bisectors
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Chapter 5: Congruent Triangles and Parallel Lines
Properties of Parallelograms; Quadrilaterals; Rectangles, Rhombuses, and Squares; Trapezoids; Midsegment Theorem; Indirect Proof; Inequalities in Triangles
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Chapter 6: Similarity
Ratio and Proportion; Properties of Proportion; Similar Polygons; AA Similarity; SAS and SSS Similarity; Segments Divided Proportionally
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Chapter 7: Right Triangles
Right Triangle Proportions; The Pythagorean Theorem; The Converse of the Pythagorean Theorem; Special Right Triangles; The Tangent Ratio; The Sine and Cosine Ratios; Angles of Elevation and Depression
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Chapter 8: Circles
Basic Terms; Tangent Lines; Common Tangents and Tangent Circles; Arcs; Chords; Inscribed Angles; Angles of Chords, Secants, and Tangents; Segments of Chords, Secants, and Tangents
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Chapter 9: Constructions and Loci
Segments, Angles, and Bisectors; Perpendicular and Parallel Lines; Circles; Special Segments; Concurrency Theorem; Simple Locus; Compound Locus; Construction and Loci
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Chapter 10: Area and Perimeter of Polygons
Rectangles; Parallelograms and Triangles; Trapezoids and Other Quadrilaterals; Regualr Polygons; Similar Polygons; Circumference and Arc Length; Circles, Sectors, and Segments
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Chapter 11: Surface Area and Volume
Surface Area of Prisms; Surface Area of Pyramids; Volume of Prisms; Volume of Pyramids; Cylinders; Cones; Spheres; Similar Solids
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Chapter 12: Coordinate Geometry
Midpoint of a Segment; Slope of a Line; Slopes of Perpendicular and Parallel Lines; Equations of Lines; The Distance Formula; The Equations of a Circle; Proofs and Proving Theorems
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Chapter 13: Transformations
Reflections and Line Symmetry; Translational Symmetry; Rotations and Rotational Symmetry; Mappings; Isometries and Congruence; Dilations; Dilations and Similarity
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