The Basic Building Blocks of Geometry Study Guide
Introduction to The Basic Building Blocks of Geometry
This lesson explains the basic building blocks of geometry: points, lines, rays, line segments, and planes. It also shows you the basic properties you need to understand and apply these terms.
The term geometry is derived from the two Greek words geo and metron. It means "to measure the Earth." The great irony is that the most basic building block in geometry, the point, has no measurement at all. But you must accept that a point exists in order to have lines and planes, because lines and planes are made up of an infinite number of points. Let's begin this lesson by looking at each of the basic building blocks of geometry.
A point has no size and no dimension; however, it indicates a definite location. Some real-life examples are a pencil point, a corner of a room, and the period at the end of this sentence. A series of points is what makes up lines, line segments, rays, and planes. There are countless points on any one line. A point is named with an italicized uppercase letter placed next to it:
If you want to discuss this point with someone, you would call it "point A."
A line is straight, but it has no thickness. It is an infinite set of points that extends in both directions. Imagine a straight highway with no end and no beginning; this is an example of a line. A line is named by any one italicized lowercase letter or by naming any two points on the line. If the line is named by using two points on the line, a small symbol of a line (with two arrows) is written above the two letters. For example, this line could be referred to as line or line :
A ray is a part of a line with one endpoint that continues indefinitely in the direction opposite the endpoint. It has an infinite number of points on it. Flashlights and laser beams are good ways to imagine rays. When you refer to a ray, you always name the endpoint first. The ray shown here is ray , not ray
A line segment is part of a line with two endpoints. It has an infinite number of points on it. A ruler and a baseboard are examples of ways you might picture a line segment. Like lines and rays, line segments are also named with two italicized uppercase letters, but the symbol above the letters has no arrows. This segment could be referred to as or :
A plane is a flat surface that has no thickness or boundaries. Imagine a floor that extends in all directions as far as you can see. Here is what a plane looks like:
When you talk to someone about this plane, you could call it "plane ABC."However, the more common practice is to name a plane with a single italicized capital letter (no dot after it) placed in the upper-right corner of the figure as shown here:
If you want to discuss this plane with someone, you would call it "plane X."
Working with the Basic Building Blocks of Geometry
Points, lines, rays, line segments, and planes are very important building blocks in geometry. Without them, you cannot work many complex geometry problems. These five items are closely related to one another. You will use them in all the lessons that refer to plane figures—figures that are flat with one or two dimensions. Later in the book, you will study three-dimensional figures—figures that occur in space. Space is the set of all possible points and is three-dimensional. For example, a circle and a square are two-dimensional and can occur in a plane. Therefore, they are called plane figures. A sphere (ball) and a cube are examples of three-dimensional figures that occur in space, not a plane.
One way you can see how points and lines are related is to notice whether points lie in a straight line. Collinear points are points on the same line. Noncollinear points are points not on the same line. Even though you may not have heard these two terms before, you probably understand the following two figures based on the sound of the names collinear and noncollinear.
A way to see how points and planes are related is to notice whether points lie in the same plane. For instance, see these two figures:
Again, you may have guessed which name is correct by looking at the figures and seeing that in the figure labeled Coplanar points, all the points are on the same plane. In the figure labeled Noncoplanar points, the points are on different planes.
Postulates and Theorems
You need a few more tools before moving on to other lessons in this book. Understanding the terms of geometry is only part of the battle. You must also be able to understand and apply certain facts about geometry and geometric figures. These facts are divided into two categories: postulates and theorems. Postulates (sometimes called axioms) are statements accepted without proof. Theorems are statements that can be proved. You will be using both postulates and theorems in this book, but you will not be proving the theorems.
Geometry is the application of definitions, postulates, and theorems. Euclid is known for compiling all the geometry of his time into postulates and theorems. His masterwork, The Elements, written about 300 b.c., is the basis for many geometry books today. We often refer to this as Euclidean geometry.
Here are two examples of postulates:
Practice problems for these concepts can be found at: The Basic Building Blocks Of Geometry Practice Questions.