• ### Course Introduction

• Time: 138 hours
• Free Certificate

In geometry we study the rules we follow when we examine spaces and objects in our world. Geometry allows us to make accurate predictions about the sizes of triangles, circles, and rectangles so we can design, build, and calculate distances. For example, geometry helps an architect design a studio, a farmer to buy the right amount of seed to plant their crops, an engineer to build a house, and a pilot to calculate the time and direction they need to fly to reach a distant 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 relationships that exist between lines and angles. For example, urban planners study lines and angles to efficiently arrange houses, buildings, roads, and highways. Our street maps, water supply, and electrical connections 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 calculate how to fit two adults, three kids, four suitcases, and a dog into your car for an upcoming trip.

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 explore the basic building blocks, vocabulary, and classifications of geometry. For example, 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 15 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, such as in chairs, tables, buildings, fences, and roadways.

In this unit, we 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 10 hours.

• ### Unit 3: Triangles, Congruence, and Other Relationships

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

We also study triangles and their various parts to make predictions about measurements and distance. For example, we can use the process of triangulation to calculate a distance when we have two known locations, such as when we need to calculate precise measurements for a land survey on a building construction site, determine distances for an upcoming boat race, or define the correct angles and distances for a rocket launch.

Completing this unit should take you approximately 17 hours.

• ### Unit 4: Triangle Relationships

In this unit, we explore triangles in more detail, including more about triangulation, mid-segments, and bisected lengths. City planners and building designers frequently 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 in the middle of the town plaza. Construction workers also use the mid-segment of a triangle to help strengthen roof trusses when they build.

Completing this unit should take you approximately 11 hours.

• ### Unit 5: Polygons and Quadrilaterals

A polygon is a shape that has no curves. In this unit we 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 12 hours.

• ### Unit 6: Similarity

In this unit, we study 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 14 hours.

• ### Unit 7: Right Triangle Trigonometry

In this unit we explore basic trigonometry which we use 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 11 hours.

• ### Unit 8: Circles

In this unit, we 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 16 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 18 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 section, we will investigate three dimensional shapes, and learn to calculate their surface areas and volumes.

Completing this unit should take you approximately 14 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.