GeoPreview Proof Terminology

Euclidean Geometry is an axiomatic system made up of a collection of statements, i.e. definitions and axioms, from which we expand the system by proving theorems based on the definitions, axioms and previously proved theorems.

• True

• False

An axiom is...

• a statement of the meaning of a word or term.

• a self-evident statement accepted as true for the purpose of reasoning. A fundamental building block of the system.

• a statement proved from other statements.

• the reverse of a statement.

Tags

CCSS.RI.8.1

CCSS.RI.8.8

CCSS.RL.11-12.1

CCSS.RL.8.1

CCSS.RL.9-10.1

A theorem is...

• a statement of the meaning of a word or term.

• the reverse of a statement.

• a statement proved from definitions, axioms and other statements. A proven rule.

• a statement of lesser importance.

A corollary is...

• an important theorem.

• the same as the converse of a theorem.

• the reverse statement.

• a theorem in its own right but of lesser importance which follows immediately from another theorem.

Tags

CCSS.RF.3.3B

CCSS.RF.3.3C

CCSS.RF.3.3D

CCSS.RF.4.3A

CCSS.RF.5.3A

A mathematical statement which is apparently true, but has not yet been proven is...

• a theory or idea.

• a theorem.

• a proposition or conjecture.

• an invalid argument.

The logical progression of statements based on definitions, axioms and other theorems to demonstrate the truth of a conjecture or proposition is known as a...

• definition.

• rider.

• solution.

• deductive proof.

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What is used to disprove a statement?

• An idea.

• A proof.

• A counter-example.

• A theorem.

Tags

CCSS.HSG.CO.B.7