• Course Introduction

        • Time: 41 hours
        • Free Certificate
        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.

        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.

        First, read the course syllabus. Then, enroll in the course by clicking "Enroll me in this course". Click Unit 1 to read its introduction and learning outcomes. You will then see the learning materials and instructions on how to use them.

      • Unit 1: The Basics of Geometry

        In this unit, we will explore the basic building blocks, vocabulary, and classifications of geometry. If you know how to identify and classify the shapes and properties of certain types of triangles, you can apply the appropriate rules and relationships to quickly and easily make predictive calculations.

        Completing this unit should take you approximately 5 hours.

      • Unit 2: Parallel and Perpendicular Lines

        Parallel lines are lines in a plane that do not intersect. Perpendicular lines intersect at a right angle: 90 degrees. We see parallel and perpendicular lines all around us in chairs, tables, buildings, fences, and roadways.

        In this unit, we will explore what happens when parallel lines cross other lines and how the angles they form relate to one another.

        Completing this unit should take you approximately 4 hours.

      • Unit 3: Triangles, Congruence, and Other Relationships

        In this unit, we will explore different methods for comparing and identifying identical triangles depending on the information we have available. Whether we compare pieces of furniture, automobiles, or pieces of a candy bar, we will have to make sure that objects are the same size and shape.

        We will also study triangles and their parts to predict their measurements and distances between them. For example, we can use the process of triangulation to calculate a distance when we have two known locations. This can be useful when we need to calculate precise measurements for a land survey on a building construction site, determine distances for a race, or calculate the correct angles for a rocket launch.

        Completing this unit should take you approximately 5 hours.

      • Unit 4: Triangle Relationships

        In this unit, we will explore triangulation, midsegments, and bisected lengths of triangles. City planners and building designers regularly need to calculate the circumcenter of a triangle, which is the point in the middle of the triangle that is equally distant from all three sides. For example, they may need to calculate whether the location of a new parking garage is the same distance from three or more companies, or whether a city monument is exactly in the middle of a plaza. Construction workers use the midsegment of a triangle to help strengthen roof trusses.

        Completing this unit should take you approximately 3 hours.

      • Unit 5: Polygons and Quadrilaterals

        A polygon is a shape that has no curves. In this unit, we will focus on quadrilaterals, which are polygons with four sides. While each has their own set of characteristics, they share some properties with other quadrilaterals.

        Completing this unit should take you approximately 4 hours.

      • Unit 6: Similarity

        In this unit, we will review how ratios and proportions connect with the concept of similarity. We frequently consider objects to be similar to one another due to their design, size, or some other quality. In geometry, however, strict rules apply for determining whether two shapes are similar.

        Completing this unit should take you approximately 5 hours.

      • Unit 7: Right Triangle Trigonometry

        In this unit we, will explore basic trigonometry. We use trigonometry for several types of measuring techniques, such as calculating the height of a building when you know how far away you are standing from a building and the angle of your gaze to the top. Sailors used trigonometry to determine distances and set their course by using the stars as their guide.

        Completing this unit should take you approximately 3 hours.

      • Unit 8: Circles

        In this unit, we will explore circles and arcs, which are slices of the edge of a circle. We use arcs to describe anything that looks like an incomplete circle, such as the feet of a rocking chair or the crust of a slice of pizza. We will learn to classify and measure arcs in this unit.

        Completing this unit should take you approximately 3 hours.

      • Unit 9: Perimeter and Area

        Calculating area and perimeter are probably the two most common applications of geometry.

        For example, if you want to install some carpet you need to measure the size of your space so you know how much carpet you need to buy to cover it (in terms of square feet or square meters). To install a fence, you need to calculate the perimeter of your yard so you know how much lumber you need to buy. To wire a room you need to calculate the perimeter of your room's interior walls so you know how much cable you need to buy and how much your labor and installation will cost (your electrician will likely charge you by the foot).

        Completing this unit should take you approximately 5 hours.

      • Unit 10: Surface Area and Volume

        We frequently need to calculate the amount of space that exists inside an object. For example, we use the concept of volume to follow a recipe, but we also use it when we need to fill a moving box with books or packages, fill a moving van with boxes or furniture, fill a simple container with water, or fill a gas tank with gasoline.

        Since containers come in so many shapes and sizes, in addition to simple square and rectangular boxes, learning how to calculate the amount of space that is available inside a three-dimensional object not only comes in handy, but can save you time, money, and create less waste.

        Similarly, you may also need to calculate the amount of space that exists on the outside of an object, such as when you decide to paint your house or office. Making a few key calculations can ensure you buy the right amount of paint you need, the first time.

        In this unit, we will investigate three dimensional shapes, and learn to calculate their surface areas and volumes.

        Completing this unit should take you approximately 4 hours.

      • Course Feedback Survey

        Please take a few minutes to give us feedback about this course. We appreciate your feedback, whether you completed the whole course or even just a few resources. Your feedback will help us make our courses better, and we use your feedback each time we make updates to our courses.

        If you come across any urgent problems, email contact@saylor.org or post in our discussion forum.

      • Certificate Final Exam

        Take this exam if you want to earn a free Course Completion Certificate.

        To receive a free Course Completion Certificate, you will need to earn a grade of 70% or higher on this final exam. Your grade for the exam will be calculated as soon as you complete it. If you do not pass the exam on your first try, you can take it again as many times as you want, with a 7-day waiting period between each attempt.

        Once you pass this final exam, you will be awarded a free Course Completion Certificate.