The purpose of deductive proof is to convince the reader.
In geometry, a deductive proof builds from one true statement to the next. Each step of reasoning must be supported with a previously confirmed conclusion, which then allows another assertion.
The process of proof
An explorative activity in geometry may lead to a conjecture about a specific result, after observing some cases when it was true and none for which it was not true. After more investigation, this conjecture may become a proposition. If the proposition can be proven through deductive reasoning it is a true result, which is called a theorem.
There is a distinct difference between a proposition and a theorem.
- A proposition is an unproven statement which is believed to be true.
- A theorem is a statement that can be demonstrated to be true.
The pathway for deductive proof leads from exploration through conjecture to proposition, and then from proposition through proof to theorem.
