Course Syllabus

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 Saylor Student Handbook.


Course Description

In this course, you will study the relationships between lines and angles. You will learn to calculate how much space an object covers, determine how much space is inside of a three-dimensional object, and other relationships between shapes, objects, and the mathematics that govern them.


Course Introduction

Geometry is the study of space (for now, mainly two-dimensional, with some three-dimensional thrown in) and the relationships of objects contained inside. It is one of the more relatable math courses, because it often answers that age-old question, "When am I ever going to use this in real life?" Look around you right now. Do you see any triangles? Can you spot any circles? Do you see any books that look like they are twice the size of other books? Does your wall have paint on it?

In geometry, you will explore the objects that make up our universe. Most people never give a second thought to how things are constructed, but there are geometric rules at play. Most people never think twice about a rocket launch, but if that rocket is not launched at an exact angle, it will miss its target. A football field has to be measured out to be a rectangle; if you used another shape, such as a trapezoid, that would give an unfair advantage to one team, because that one team would have more space to work with.

In this course, you will study the relationships between lines and angles. Have you ever looked at a street map? Believe it or not, there is a lot of geometry on a map, as you will see from this course. You will learn to calculate how much space an object covers, which is useful if you ever have to, say, buy some paint. You will learn to determine how much space is inside of a three-dimensional object, which is useful for those times you are trying to fit four suitcases, three kids, two adults, and a dog into the back of your vehicle.

This course is comprised of 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'll also see related learning outcomes identified in each unit. You can use the learning outcomes to help organize your learning and gauge your progress.


Course Materials

The primary learning materials for this course are readings, lectures, video tutorials, and other resources.

All course materials are free to access, and can be found through the links provided in each unit and subunit of the course. Pay close attention to the notes that accompany these course materials, as they will instruct you as to what specifically to read or watch at a given point in the course, and help you to understand how these individual materials fit into the course as a whole. You can also access a list all of the materials used in this course by clicking on Resources in the course's "Activities" menu.


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 tabulated as soon as you complete it. If you do not pass the exam on your first attempt, you may take it again as many times as needed, following a 7-day waiting period between each attempt. Once you have successfully passed the final exam you will be awarded a free Saylor Certificate of Completion.

Any unit assessments and other types of quizzes in this course are intended to help you to gauge how well you are learning and do not factor into your final course grade. You may retake all of these as many times as needed to feel that you have an understanding of the concepts and material covered. You can locate a full list of these sorts of assessments by clicking on Quizzes in the course's "Activities" menu.


Tips for Success

RWM103: Geometry is a self-paced course in which you the learner determines when you will start and when you will complete the course. There is no instructor or predetermined schedule to follow. While learning styles can vary considerably and any particular student will take more or less time to learn or read, 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 (daily, or at least weekly) 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 below we've compiled a few suggested study strategies to help you succeed:

  • Take notes on the various terms, practices, and theories as you read. This can help you differentiate and contextualize concepts and later provide you with a refresher as you study.
  • As you progress through the materials, take time to test yourself on what you have retained and how well you understand the concepts. The process of reflection is important for creating a memory of the materials you learn; it will increase the probability that you ultimately retain the information.
  • Although you may work through this course completely independently, you may find it helpful to connect with other Saylor Academy students through the discussion forums. You may access the discussion forums at


Suggested Prerequisites
In order to take this course, you should have completed courses RWM101: Foundations of Real World Math and RWM102: Algebra

Technical Requirements

This course is delivered fully 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, free of charge, here. Although you can access some course resources without being logged into your account, it's advised that you log in to maximize your course experience. For example, some of the accessibility and progress tracking features are only available when you are logged in.

For additional technical guidance check out Saylor Academy's tech-FAQ and the Moodle LMS tutorial.


There is no cost to access and enroll in this course. All required course resources linked throughout the course, including textbooks, videos, webpages, activities, etc are accessible for no charge. This course also contains a free final exam and course completion certificate.

Last modified: Thursday, April 9, 2020, 6:49 PM