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# Geometric proof

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.

## Convince me

Proof is more than a demonstration of a result or a reasonable argument supporting its truth.