Home > Geometric reasoning > Big ideas > Geometric proof

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.

Curriculum links

Year 7: Demonstrate that the angle sum of a triangle is 180° and use this to find the angle sum of a quadrilateral.

Year 10: Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes.