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Although we may not always recognize it, we use basic geometry skills regularly in everyday life. For instance, we consider whether a picture on the wall is parallel with the floor, or we calculate the area of a room when installing new carpeting.
Geometry is also an integral part of many other areas of study, including physics and other natural sciences. This course provides a more rigorous mathematical foundation for both practical and theoretical geometric thinking.
The course begins by considering basic figures such as points, lines, and planes, and then expands into the concepts of parallelism and perpendicularity as well as more complicated geometric figures such as polygons (triangles, quadrilaterals, and so on) and circles. The course considers mainly two-dimensional figures, but two lessons on three-dimensional geometry provide more complete coverage of the subject.
Each successive lesson in the course builds on previous lessons, culminating in lessons that teach the student how to calculate lengths, areas, and volumes of more complicated figures. In addition to its in-depth discussion of the mathematical aspects of geometry, the course also includes lessons on how to draw various figures using a compass and straightedge as well as a lesson on strategy for solving real-world geometry problems.
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Lesson 1 - Geometry Terms and MotivationTo begin the course, we first discuss why the study of geometry can be beneficial, both in school and work as well as in daily life.
Lesson 2 - Geometric Reasoning and MeasurementTo aid in our discussion of geometry, this lesson reviews some fundamental principles of geometric reasoning and measurement that will aid our analysis throughout the course.
Lesson 3 - Angles and ParallelismIn this lesson, we introduce the concept of an angle and discuss the relationships among angles formed by intersecting lines.
Lesson 4 - Triangles I: Properties of TrianglesThis lesson introduces our first polygon: the triangle. We consider what constitutes a triangle as well as several types of triangles with special properties.
Lesson 5 - Triangles II: Congruent TrianglesThis lesson uses concepts from our introduction to triangles in the previous lesson and applies them to congruent triangles.
Lesson 6 - Triangles III: Similar TrianglesThis lesson concludes our focus on triangles by considering another sense in which we can understand congruence and similarity
Lesson 7 - QuadrilateralsThis lesson introduces quadrilaterals, or four-sided polygons. We study the basic properties of quadrilaterals and go on to identify special quadrilaterals and to derive formulas for their areas.
Lesson 8 - PolygonsHaving studied three- and four-sided figures (polygons), we now turn to arbitrary n-sided polygons.
Lesson 9 - CirclesThe course now turns from polygons to circles. A circle is vastly different from a polygon, and it requires a different approach to understanding its properties and calculating corresponding values.
Lesson 10 - Composite FiguresThis lesson combines the principles of previous lessons and applies them to composite figures, which are composed of (or can be broken down into) various simpler figures.
Lesson 11 - Classical ConstructionThis lesson takes a slight break from the analytical approach to geometry and considers how to perform some simple "classical constructions" using a pencil, compass, and straightedge.
Lesson 12 - Practical Geometry ProblemsThis lesson takes a break from introducing new geometry concepts and turns instead to application of what we already know to practical situations.
Lesson 13 - Three-Dimensional Geometry IIn this lesson, we introduce three-dimensional geometry as an extension of two-dimensional geometry.
Lesson 14 - Three-Dimensional Geometry IIIn this lesson, we extend our knowledge of two-dimensional geometry and what we have learned thus far about three-dimensional geometry to the analysis of simple polyhedra as well as spheres and cylinders.
Lesson 15 - Geometry and TrigonometryIn this lesson, we introduce trigonometry, which expands on our knowledge of circles, angles, triangles, and other aspects of geometry.
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Learning OutcomesBy successfully completing this course, students will be able to:
- Define basic geometry terms.
- Define geometric reasoning and measurement.
- Describe angles and parallelism.
- Describe properties of triangles.
- Describe congruent triangles.
- Describe similar triangles.
- Solve problems involving Quadrilaterals.
- Solve problems involving Polygons.
- Solve problems involving circles.
- Describe classical construction.
- Solve practical geometry problems.
- Describe three-dimensional geometry, and
- Demonstrate mastery of lesson content at levels of 70% or higher.
|Lesson 1 Assignment||Assignment||10|
|Lesson 1B Assignment||Assignment||25|
|Lesson 1 Geometry Terms and Motivation||Exam||10|
|Lesson 2 Assignment||Assignment||20|
|Lesson 2 Geometric Reasoning and Measurement||Exam||10|
|Lesson 3 Assignment||Assignment||20|
|Lesson 3B Assignment||Assignment||25|
|Lesson 3 Angles and Parallelism||Exam||9|
|Lesson 4 Assignment||Assignment||25|
|Lesson 4 Triangles I: Properties of Triangles||Exam||10|
|Lesson 5 Assignment||Assignment||25|
|Lesson 5 Triangles II: Congruent Triangles||Exam||10|
|Lesson 6 Assignment||Assignment||25|
|Lesson 6 Triangles III: Similar Triangles||Exam||7|
|Lesson 7 Assignment||Assignment||20|
|Lesson 7 Quadrilaterals||Exam||10|
|Lesson 8 Assignment||Assignment||20|
|Lesson 8B Assignment||Assignment||25|
|Lesson 8 Polygons||Exam||10|
|Lesson 9 Assignment||Assignment||20|
|Lesson 9 Circles||Exam||10|
|Lesson 10 Assignment||Assignment||20|
|Lesson 10 Composite Figures||Exam||10|
|Lesson 11 Assignment||Assignment||20|
|Lesson 11 Classical Construction||Exam||10|
|Lesson 12 Assignment||Assignment||20|
|Lesson 12B Assignment||Assignment||25|
|Lesson 12 Practical Geometry Problems||Exam||10|
|Lesson 13 Assignment||Assignment||20|
|Lesson 13 Three-Dimensional Geometry I||Exam||10|
|Lesson 14 Assignment||Assignment||20|
|Lesson 14 Three-Dimensional Geometry II||Exam||10|
|Lesson 15 Assignment||Assignment||20|
|Lesson 15 Geometry and Trigonometry||Exam||10|
|The Final Exam||Exam||43|
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- Pre-Algebra 101$75.001.4 CEUs
- Geometry 101: Beginner to Intermediate Level$110.001.4 CEUs
- Statistics 101$120.003.5 CEUs
- Precalculus 101$110.003.5 CEUs
- Basic Math 101$75.002.1 CEUs
- ABCs of Algebra$75.003.0 CEUs
- Math All-In-One (Arithmetic, Algebra, and Geometry Review)$110.003.5 CEUs
- ABCs of Geometry$75.001.3 CEUs
- Applied Statistics 101$95.003.5 CEUs
- Business Math 101$60.001.2 CEUs
- Business Analysis 101$65.001.2 CEUs