1.1  Introduction & Fundamental ideas

Geometry:

Geometry is the study of the properties and measurements of flat figures, such as points, lines, angles, triangles, and circles, and of solid figures, such as cubes, cones, and pyramids. The subject is not made up of material that you have never had experience with as you have had some experience with geometry in some of your previous classes. Geometry uses arithmetic and algebra to express properties and characteristics of the figures we study, however it is not necessarily concerned with values ( numbers ) or equations.

Before we begin our study of geometry, we must make sure that we "Say what we mean and mean what we say". Familiar terms must be carefully defined, ideas illustrated, and fundamental truths examined and accepted.

Definitions, Postulates, & Theorems:

these are the basic building blocks used in geometry

• Definitions:  A definition of a term is a statement that defines a mathematical object. Definitions usually reference other mathematical terms.
  
  
• Postulates:  Postulates, or Axioms, are assumed to be true.  Why you ask? Because they just are!
  
  
• Theorems:  Theorems need to be proven as true based upon Postulates and other Proven Theorems.
  

Undefined Terms:

Now I know that this sounds like we are not following the rules so to speak, but there are three undefined terms that are required and necessary building blocks.

• Point:  A point names a location and has no size. It is represented by a dot and labeled using a capital letter, such as P.
  
  
• Line:  A line is a straight path that has no thickness and extends forever. There are an infinite number of points on a line. A line is named using either a lowercase letter or any two points on the line.
  
  
• Plane:  A plane is a flat surface that has no thickness and extends forever. A plane is named using either an uppercase letter or three noncollinear points that lie in the plane.

Proofs:

These are logical arguments used to prove theorems.  In other word proofs are used for the construction of geometric ideas using the building blocks of things we already know.  When we finish building  a proof we have a new theorem that can be used.

Or put another way...

A proof is like a Recipe for making a cake, Plans / Blue-Prints for making a cabin or tiny house, Patterns for making clothes, or a Program to control a robot.

In each case the information is used to make sure that the end result is always the same when given the material needed for each application.

Formulas:

These are used to represent relationships between different objects in geometry.  There are many formulas to be found in geometry.  So when in doubt ALWAYS write them out, draw out a picture of the situation, and give your self an example to look at.

...and so it begins...