Course Description
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.
- Completely Online
- Self-Paced
- 6 Months to Complete
- 24/7 Availability
- Start Anytime
- PC & Mac Compatible
- Android & iOS Friendly
- Accredited CEUs
Learning Outcomes
- Identify and describe fundamental geometric figures such as points, lines, rays, and planes by illustrating them accurately with examples.
- Recognize the importance of geometry in daily life, academia, and professional settings by providing three examples of practical applications.
- Define deductive reasoning and demonstrate deriving conclusions from given premises.
- Explain the importance of units in geometric measurement and demonstrate using arbitrary units for measurement.
- Recognize and construct a two-column proof for basic geometric problems.
- Demonstrate understanding of angle relationships and properties when a transversal intersects two parallel lines.
- Identify and calculate the measures of angles formed by intersecting lines using degree measurements.
- Calculate the length of a side in a right triangle using the Pythagorean theorem.
- Identify and classify triangles as equilateral, isosceles, or scalene based on side lengths and angles.
- Demonstrate congruence between two triangles using the hypotenuse-leg (HL) condition in right triangles.
- Recognize and justify the four conditions (SSS, SAS, ASA, AAS) for triangle congruence through geometric reasoning.
- Prove the similarity of any two given triangles by applying the appropriate conditions such as angle-angle, side-side-side proportionality, or side-angle-side proportionality.
- Demonstrate how to use geometric transformations to show two triangles are similar, including dilation and translation, within a structured problem-solving process.
- Demonstrate mastery of lesson content at levels of 70% or higher.
Assessment Guide
| Assessment | Points |
|---|---|
| Lesson 1 Assignment | 1 points |
| Lesson 1 Geometry Terms and Motivation | 10 points |
| Lesson 1 Exercises | 5 points |
| Lesson 2 Activity | 1 points |
| Lesson 2 Geometric Reasoning and Measurement | 10 points |
| Lesson 3 Angles and Parallelism | 9 points |
| Lesson 4 Activity | 1 points |
| Lesson 4 Triangles I: Properties of Triangles | 10 points |
| Lesson 4 Exercises | 3 points |
| Lesson 5 Activity | 1 points |
| Lesson 5 Triangles II: Congruent Triangles | 10 points |
| Lesson 5 Exercises | 3 points |
| Lesson 6 Triangles III: Similar Triangles | 7 points |
| Lesson 7 Quadrilaterals | 10 points |
| Lesson 8 Polygons | 10 points |
| Lesson 8 Exercises | 7 points |
| Lesson 9 Activity | 1 points |
| Lesson 9 Circles | 10 points |
| Lesson 10 Composite Figures | 10 points |
| Lesson 11 Classical Construction | 10 points |
| Lesson 12 Activity | 1 points |
| Lesson 12 Practical Geometry Problems | 10 points |
| Lesson 13 Activity | 1 points |
| Lesson 13 Three-Dimensional Geometry I | 10 points |
| Lesson 14 Three-Dimensional Geometry II | 10 points |
| Lesson 15 Geometry and Trigonometry | 10 points |
| The Final Exam | 43 points |
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