Welcome to MA008: Real World Math: 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.

Course Description

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.

Course Introduction

In geometry, we study the rules of the spaces and objects in our world. Geometry allows us to 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. Artists also use geometry, as you can see in this picture by M. C. Esher.

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 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 angles created by parallel lines;
  • Determine if two given figures are similar;
  • Use trigonometric ratios and the Pythagorean theorem to solve right triangles;
  • Use relationships among inscribed angles, radii, and chords to find missing angle measurements;
  • Find the volume of cylinders, pyramids, cones, and spheres;
  • 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.

Course Materials

This course's primary learning materials 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 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 at this link.

Some parts of this course may have been created or reviewed with the support of artificial intelligence (AI). To make sure you receive accurate, high-quality, and academically sound learning materials, all AI-assisted content is carefully checked and approved by Saylor Academy's faculty and subject matter experts.

Evaluation and Minimum Passing Score

Only the final exam is considered when awarding you a grade for this course. To pass this course, you will need to earn a grade of 70% or higher on the final exam.

Your score on the exam will be calculated as soon as you complete it. Be sure to study in between each attempt! If you do not pass the exam, you will not complete this course or receive a certificate of completion. You can attempt the exam as many times as you want.

There are end-of-unit assessments in this course that are designed to help you study and do not factor into your final course grade. You can take them as many times as you want until you understand the concepts they cover.

You can see all of these assessments at this link.

Continuing Education Credits

The certificate earned by passing this self-paced course displays the program hours you completed and continuing education credits (CEUs). CEUs document successful completion of courses that are designed to improve the knowledge and skills of working adults. Many industries value CEUs, and now your certificate reflects them clearly, and they may be used to support career advancement or to meet professional licensing standards. This course contains 4.8 CEUs.

Tips for Success

MA008: Real World Math: Geometry is a self-paced course, meaning you can decide when to start and complete the course. We estimate the "average" student will take hours to complete. We recommend studying at a comfortable pace and scheduling your study time in advance.

Learning new material can be challenging, so here are a few study strategies to help you succeed:

  • Take notes on terms, practices, and theories. This helps you understand each concept in context and provides a refresher for later study.
  • Test yourself on what you remember and how well you understand the concepts. Reflecting on what you've learned improves long-term memory retention.

Technical Requirements

This course is delivered entirely online. You will need access to a computer or web-capable mobile device and consistent internet access to view or download resources and complete auto-graded assessments and the final exam.

To access the full course, including assessments and the final exam, log into your Saylor Academy account and enroll in the course. If you don't have an account, you can create one for free here. Note that tracking progress and taking assessments require you to log in.

For more details and guidance, please review our complete Technical Requirements and our student Help Center.

Optional Saylor Academy Mobile App

You can access all course features directly from your mobile browser, but if you have limited internet connectivity, the Saylor Academy mobile app provides an option to download course content for offline use. The app is available for iOS and Android devices.

Download on Google Play Download on the App Store

Fees

This course is entirely free to enroll in and access. All course materials, including textbooks, videos, webpages, and activities, are available at no charge. This course also contains a free final exam and a free course completion certificate.