Topic outline

  • Course Introduction

    "Everything is numbers.”  This phrase was uttered by the lead character, Dr. Charlie Epps, on the hit television show "NUMB3RS.”  If everything has a mathematical underpinning, then it follows that everything is somehow mathematically connected, even if it is only in some odd, "six degrees of separation (or Kevin Bacon)” kind of way.

    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.

    These are just some of the topics you will be learning.  As you will quickly see, everything is not just numbers; it is also relationships.  Even nature itself knows this.  What did the little acorn say when it grew up?  "Gee, I'm a tree!”

    Pages: 2
  • Unit 1: The Basics of Geometry

    From a young age, we learn basic vocabulary and basic concepts that lead us to understand greater concepts.  In this unit, you will learn about the basic building blocks of Geometry.

    Everything has a proper name.  We often seem to use nicknames: "fridge” instead of "refrigerator,” "phone” instead of "telephone,” and so on.  Still, we know what the proper terminology is, even if we do not use it as often as we probably should.  Knowing the meanings of several basic terms in Geometry is important, because these terms are going to keep popping up over and over again.  Whether it is knowing a simple definition, or understanding the relationships between angles, these basic items are a "must know” in Geometry.

    In life, we also classify things.  We tend to classify by height, age, weight, food preference, nationality, etc.  We will use pretty much anything we can think of for classification purposes.  While some classifications might seem unnecessary to us, others seem quite important.  Classifying berries, for example, can help you to keep from eating a poisonous one that would make you sick.  Without classification, we would not have a way to keep the good ones separate from the bad ones.  The same holds true in Geometry.  Classifying shapes like triangles can help us recognize these shapes faster and eventually recognize the rules and relationships pertaining to their classification.

    Page: 1
  • Unit 2: Parallel and Perpendicular Lines

    Simply put, parallel lines are lines in a plane that do not intersect, while perpendicular lines are lines that intersect at a right angle (90°).  Parallel and perpendicular lines are all around us.  For example, railroad tracks, iron fencing, latticework, and kitchen tables all have parallel and/or perpendicular lines.

    Have you ever looked at a tile floor that has an intricate pattern of crisscrossing lines?  The pattern has to be carefully replicated, following special rules.  When parallel lines cross other lines, they create their own set of special rules, which may be used in making these patterns.  In this unit, you will learn what happens when parallel lines cross other lines and how all the created angles relate to each other.

    Page: 1
  • Unit 3: Triangles, Congruence, and Other Relationships

    Making sure that objects are of equal size is important in life.  Whether pieces of furniture, automobiles, or just pieces of a candy bar shared between siblings, we often have to make sure objects are the same size and shape.

    Have you ever had to prove something to a child?  Sometimes, the best way to do that is to give the child a series of logical statements and then show how it all summarizes to one conclusion.  In this unit, you will focus on showing that two triangles are identical.  There are different methods to doing this, and the one you use will depend upon the information you have available to you.  It is nothing more than following a series of logical statements and then showing how the statements draw a conclusion.

    In this unit, you will also learn more about triangles and their various parts.  Triangles, believe it or not, are used more often in life than you might think.  Triangles are often used to estimate distances.  The process of triangulation has been used for over two thousand years; with this technique, we can use two known locations and determine the distance to a location that we can see but cannot necessarily get to, like a boat out in a lake.  Today, we use triangulation for navigating boats, surveying land, launching model rockets, and other activities.

    We can also use triangles to map things out.  For example, city planners often use the circumcenter of a triangle, which is a point in the middle that is equally distant from all three sides.  They might use this to determine the location of a major parking garage, so that it is the same distance from three different companies, or they might want to make sure that a city monument is in the middle of a town plaza.

    If you live in a house, triangles are right over your heads.  Construction workers use the midsegment of a triangle to help strengthen roof trusses when they build.  If the truss is not supported properly, it could collapse, leading to lots of problems for the poor homeowner.

    Page: 1
  • Unit 4: Triangle Relationships

    In this unit, you will learn more about triangles and their various parts.  Triangles, believe it or not, are used more often in life than you might think.  Triangles are often used to estimate distances.  The process of triangulation has been used for over two thousand years; with this technique, we can use two known locations and determine the distance to a location that we can see but cannot necessarily get to, like a boat out in a lake.  Today, we use triangulation for navigating boats, surveying land, launching model rockets, and other activities.

    We can also use triangles to map things out.  For example, city planners often use the circumcenter of a triangle, which is a point in the middle that is equally distant from all three sides.  They might use this to determine the location of a major parking garage, so that it is the same distance from three different companies, or they might want to make sure that a city monument is in the middle of a town plaza.

    If you live in a house, triangles are right over your heads.  Construction workers use the midsegment of a triangle to help strengthen roof trusses when they build.  If the truss is not supported properly, it could collapse, leading to lots of problems for the poor homeowner.

    Page: 1
  • Unit 5: Polygons and Quadrilaterals

    Polygons are everywhere around us.  If you see a shape that has no curves, then it is a polygon.  As a child, you probably learned the names of many common polygons.  In this unit, you will focus on quadrilaterals, which are polygons with four sides.  They each have their own set of characteristics and share some characteristics with other quadrilaterals.  You will learn to recognize these characteristics and to use them to help you answer questions about quadrilaterals.

    Page: 1
  • Unit 6: Similarity

    In this unit, you will review ratios and proportions, and you will learn how they connect to similarity.  In the real world, you may see an item and think that it is similar to something else, whether it is because of the design, the size, or some other factors.  In Geometry, however, similarity has very strict rules attached to it.  You will learn to apply these rules to determine if two shapes, especially triangles, are similar.

    Page: 1
  • Unit 7: Right Triangle Trigonometry

    In this unit, you will learn the basics of trigonometry.  Trigonometry is used for several different measuring techniques.  You can determine the height of a building, for example, if you know how far away you are standing and at what angle your eyes form when looking up to its top.  In previous centuries, mariners could use trigonometry to help them set their course, using the heavens as a guide.

    Page: 1
  • Unit 8: Circles

    Circles are everywhere you look, for example, tires, pools, fans, and watches.  You can probably think of several more items that are circular.  In this unit, you will learn about circles and arcs, which are slices of the edge of a circle.

    Believe it or not, arcs are used a lot in real life.  The feet of a rocking chair are arcs; the crust on a slice of pizza is an arc.  Anything that looks like an incomplete circle is an arc.  How are these arcs made?  What kinds are there?  How can we measure them?  These are questions that you will explore in this unit.

    Page: 1
  • Unit 9: Perimeter and Area

    Two of the most common applications of Geometry are area and perimeter.  Owning a home gives you plenty of opportunities to use these concepts.  Thinking of buying a cordless electric lawnmower?  The manufacturer will give you an estimate of the mower's battery life using square feet.  If your yard is extremely large and your mower's battery life is not long enough, it might take you multiple sessions to get it all mowed.  Are you buying new carpeting for your home?  It is sold in square feet or square yards.  You definitely do not want to buy too much carpeting or too little carpeting.  You are not just going to eyeball it and make a guess.  You will want to measure everything carefully, and then order a bit more, giving yourself some leeway.

    Like area, perimeter is often used in home ownership.  If you install fencing around your yard, you are going to calculate the perimeter before you buy the fencing.  If you are forced to run wiring around the walls of a room, it is vital that you know how much wiring you will need.

    Page: 1
  • Unit 10: Surface Area and Volume

    Finding the amount of space inside of an object is important, and something you will do in your everyday life.  If you try to fill a box with DVDs, to fill up a sandbox, or to fill a pool with water, you will use concept of volume.  There are more shapes than just simple boxes, so you will learn to find the amount of space inside different types of three-dimensional objects.

    Finding the amount of space on the outside of an object is also something you will do in your everyday life.  If you decide to paint your house, you need to know how much space is going to be painted; buying too much paint would be a waste of money, and buying too little paint would be a nuisance.  A few minutes of calculating can ensure that you get the amount of paint you need.

    Page: 1
  • Course Evaluation Survey

    Please take a few moments to provide some feedback about this course at the link below. Consider completing the survey whether you have completed the course, you are nearly at that point, or you have just come to study one unit or a few units of this course.

    Link: Course Evaluation Survey (HTML)

    Your feedback will focus our efforts to continually improve our course design, content, technology, and general ease-of-use. Additionally, your input will be considered alongside our consulting professors' evaluation of the course during its next round of peer review. As always, please report urgent course experience concerns to contact@saylor.org and/or our Discourse forums.

  • Final Exam

    Quiz: 1