Two Column Proofs
What is a Proof?
A Proof is a convincing mathematical argument.
......(YES WRITE THIS DOWN)
This means that any person, who understands the terminology, accepts the definition and premises of the mathematics involved and thinks in a logical correct fashion could not deny the validity of the conclusions drawn.
Can be described but not given precise definitions using simple known terms .
These are intangible concepts that serve as a foundation. (Used for visualization )
Space- the set of all points
Geometric Figure- Any collection of points
Check all that are intangible concepts
CONPONENTS OF A PROOF
Geometric Proof premises
previous proven theorems
Results that we declare from the undefined terms, definitions, postulates , or results that follow from them are call a Theorem
Theorem- is a mathematical Statement that can be proven.
Postulates are statements that we assume to be true.
An postulate states relationships among defined and undefined terms. The purpose stating postulates is to establish some first principles upon which the subject of geometry is based.
A convincing mathematical argument.
Writing a Proof
Writing a Proof
Justify each logical step with reason.
You can use symbols and abbrev, but they must be clear and able to understand.
Follow these steps....
Step 1 - Write the conjecture (an opinion or conclusion formed on the basis of incomplete information.)
Step 2 - Draw the diagram
Step 3 - State the Given information and mark it on the diagram
Step 4 - State the conclusion of the conjecture in terms of Diagram
LET'S DO SOME EXAMPLES!