Welcome to RWM103: Geometry
Specific information about this course and its requirements can be found below. For more general information about taking Saylor Academy courses, including information about Community and Academic Codes of Conduct, please read the Student Handbook.
Study the relationships between lines and angles, learn to calculate how much space an object covers, determine how much space is inside of a three-dimensional object, and explore other relationships between shapes, objects, and the mathematics that govern them.
In geometry, we study the rules of the spaces and objects in our world. Geometry lets us make accurate predictions about the sizes of triangles, circles, and rectangles, which lets us calculate, design, and build. Geometry helps architects design studios, farmers buy the right amount of seeds for their land, engineers build houses, and pilots calculate the amount of time they need to fly to reach another city. We use geometry to calculate how much paint we need to buy to cover a wall and the exact angle we should use to launch a rocket to hit a distant target.
In this course, we also study the relationships that exist between lines and angles. Urban planners study lines and angles to efficiently arrange houses, buildings, roads, and highways. Our street maps, water supply, and electrical connections all depend on these precise geometric calculations. How much space is inside a three-dimensional object? You may not realize you are using principles of geometry when you are getting ready for a trip and you need to calculate how to fit two adults, three kids, four suitcases, and a dog into your car.
This course includes the following units:
- Unit 1: The Basics of Geometry
- Unit 2: Parallel and Perpendicular Lines
- Unit 3: Triangles, Congruence, and Other Relationships
- Unit 4: Triangle Relationships
- Unit 5: Polygons and Quadrilaterals
- Unit 6: Similarity
- Unit 7: Right Triangle Trigonometry
- Unit 8: Circles
- Unit 9: Perimeter and Area
- Unit 10: Surface Area and Volume
Course Learning Outcomes
Upon successful completion of this course, you will be able to:
- identify angles, rays, line segments, and points, based on the undefined notions of point, line, distance along a line, and distance around a circular arc;
- determine if figures are congruent;
- calculate distances and angles created by parallel lines;
- use the definition of congruence to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent;
- explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence;
- determine if two given figures are similar;
- use the properties of similarity transformations to establish the AA criterion for two triangles to be similar;
- explain and use the relationship between the sine and cosine of complementary angles;
- use trigonometric ratios and the Pythagorean theorem to solve right triangles in applied problems;
- describe relationships among inscribed angles, radii, and chords;
- use volume formulas for cylinders, pyramids, cones, and spheres to solve problems;
- identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects;
- describe objects using geometric shapes, their measures, and their properties;
- use the formulas for the area and circumference of a circle to solve problems;
- solve simple equations for an unknown angle in a figure using facts about supplementary, complementary, vertical, and adjacent angles; and
- solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
Throughout this course, you will also see learning outcomes in each unit. You can use those learning outcomes to help organize your studies and gauge your progress.
The primary learning materials for this course are articles, lectures, and videos.
All course materials are free to access and can be found in each unit of the course. Pay close attention to the notes that accompany these course materials, as they will tell you what to focus on in each resource, and will help you to understand how the learning materials fit into the course as a whole. You can also see a list of all the learning materials in this course by clicking on Resources in the navigation bar.
Evaluation and Minimum Passing Score
Only the final exam is considered when awarding you a grade for this course. In order to pass this course, you will need to earn a 70% or higher on the final exam. Your score on the exam will be calculated as soon as you complete it. If you do not pass the exam on your first try, you may take it again as many times as you want, with a 7-day waiting period between each attempt. Once you have successfully passed the final exam you will be awarded a free Course Completion Certificate.
Tips for Success
RWM103: Geometry is a self-paced course, which means that you can decide when you will start and when you will complete the course. There is no instructor or an assigned schedule to follow. We estimate that the "average" student will take 41 hours to complete this course. We recommend that you work through the course at a pace that is comfortable for you and allows you to make regular progress. It's a good idea to also schedule your study time in advance and try as best as you can to stick to that schedule.
Learning new material can be challenging, so we've compiled a few study strategies to help you succeed:
- Take notes on the various terms, practices, and theories that you come across. This can help you put each concept into context, and will create a refresher that you can use as you study later on.
- As you work through the materials, take some time to test yourself on what you remember and how well you understand the concepts. Reflecting on what you've learned is important for your long-term memory, and will make you more likely to retain information over time.
In order to take this course, you should:
This course is delivered entirely online. You will be required to have access to a computer or web-capable mobile device and have consistent access to the internet to either view or download the necessary course resources and to attempt any auto-graded course assessments and the final exam.
- To access the full course including assessments and the final exam, you will need to be logged into your Saylor Academy account and enrolled in the course. If you do not already have an account, you may create one for free here. Although you can access some of the course without logging in to your account, you should log in to maximize your course experience. For example, you cannot take assessments or track your progress unless you are logged in.
For additional guidance, check out Saylor Academy's FAQ.
This course is entirely free to enroll in and to access. Everything linked in the course, including textbooks, videos, webpages, and activities, is available for no charge. This course also contains a free final exam and course completion certificate.