What are the Basic Elements of Reasoning ?
There are four basic elements used in geometry. If we say studying geometry is like building a house, then these elements are like different types of materials. Logical methods of reasoning can bind these elements together and allow us to build on our foundation to create a wide range of structures. The four basic elements are the following:
1. Undefined Term : A word is so fundamental that it cannot be satisfactorily be defined. However, undefined terms can be described. Example: point, line, and plane.
2. Definition : A definition clearly states the meaning of a term or an idea. The reverse of a definition must be also true. Definitions begin by identifying the term to be defined. We state the characteristics of the term which have been previously defined or are commonly understood. Defined terms are words or symbols people use which refer to geometric figures and relationships. Example: segment, ray and angle.
3. Postulate (sometimes referred to as an "axiom") : A postulate is a statement that is based on experience and people take for granted.
4. Theorem : A theorem is a generalization which can be proven true by means of other true statements.