Having good definitions is very important in understanding geometry. Copy the table below to your notes. As you learn a new vocabulary word, record it in your notes by writing the word, the given definition, drawing a picture, recording any symbol associated with it, and writing the definition in your own words.

 Vocabulary word Given Definition Picture Symbol Definition according to you 1. 2.

Geometry literally translates from two Greek root words: "geo," meaning earth; and “metry,” meaning measure. Geometry is that part of mathematics that addresses questions related to size, shape, measure, location, and properties of figures and space.

In the 3rd century, a Greek mathematician named Euclid created a mathematical system that we now call Euclidean geometry, or plane geometry.  The Euclidean geometry mathematical system is an axiomatic system. An axiomatic system consists of undefined terms, clearly stated definitions, a list of intuitive assumptions, called postulates (or properties); and theorems, or new geometric theory statements that can be validated.  The axiomatic validation process for theorems is based on logical and deductive thinking methods.

Deductive thinking is the process of reasoning that begins with a conjecture and states known facts to support it with the goal to prove it to be true. When you use the deductive thinking method effectively, you can say “therefore” the conclusion, or conjecture, is true with certainty. If your facts are valid, then your conclusions will be valid.

Geometry is a language with special codes, symbols, figures, and vocabulary used to explain why things work.  So, it is important to understand the pieces of geometry before moving on to the problems.

### The Undefined Terms

Geometry classifies points, lines, planes, and space as undefined terms because it is easier to understand what they are from a description of their properties, than to attempt to give them a precise definition.

#### A Point

Take a moment to close your eyes and imagine the smallest particle you can, smaller than the tip of a pencil, smaller than the tip of a safety pin, smaller that an atom floating around in the air, so small that you can’t see it, but it holds a location.  It is in a unique location meaning it is the only “thing” that can occupy that spot.  This imagined object is called a point.

A point has no thickness, length or width.  It has no measure in any direction and is considered to be zero dimensional.

A point is represented by a “dot” and labeled by a capital letter.

#### A Line

When two or more points sit next to each other, they begin to form a line.  A line has no thickness or width. It does have length, but the length extends infinitely in both directions, so its measure is infinite.  Since a line has length, it is considered to be one dimensional.

A line is represented by a “line” with arrows on both ends and is labeled by any two points that lie on the line.

Two words that are often used to describe points are collinear and non-collinear.

• Collinear points lie on the same line.
• Non-collinear points do not all lie on a single line.

#### A Plane

A plane has length and width, but no thickness or height.  It is like a flat surface that extends infinitely in all directions along its length and width.  Since a plane has length and width, it is considered two dimensional.  However, just like a point and a line, it is considered an undefined term in Geometry.

A plane is represented by a four sided figure drawn in perspective and labeled by a cursive letter.

A word often used to describe points lying in the same plane is coplanar.

• Coplanar points lie in the same plane.  Coplanar points can be collinear or non-collinear.

What happens when you place points next to each other in all directions, as well as on top of and underneath each other?  You create space (the third dimension).

#### Space

Geometric space is the infinite set of all points everywhere in all directions.  Geometric solid figures are displayed in space.