Euclidean Geometry 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.

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.

"If A then B" represents a theorem. This implies that "if B then" A represents...

• a theorem as well.

• a proof.

• a corollary.

• the converse which may or may not be necessarily true.

Which of the statements below represents the converse of the following statement: If two sides of a triangle are equal in length then the angles facing those sides are equal in size.

• If two angles of a triangle are equal in size then the two sides of the triangle facing those angles are equal in length.

• If two angles of a triangle are equal in size then that triangle is an isosceles triangle.

• If two angles of a triangle are equal in size then the two sides of the triangle facing those angles are different lengths.

• The statement does not have a converse.

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.

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.

What is used to disprove a statement?

• An idea.

• A proof.

• A counter-example.

• A theorem.

"Every prime number is odd" is a proposition. Which of the following represents a counter-example to this statement?

• 2

• 4

• 6

• -2