Question

True or false: geometry is an axiomatic system where the accepted principles are undefined terms 0 and 1.

A. The statement is false. Algebra is an axiomatic system where the accepted principles are undefined terms 0 and 1.

B. The statement is true.

C. The statement is false. Geometry is an axiomatic system where the accepted principles are the undefined terms point, line and plane.

D. The statement is false. Geometry is an axiomatic system where the accepted principles are the undefined terms circle, triangle, and square

Answer 1

C. The statement is false. Geometry is an axiomatic system where the accepted principles are the undefined terms point, line and plane.

Explanation:

The 4 basic characteristics of axiomatic systems are:

• Undefined terms (or primitive terms)
• Axioms (or postulates)
• Theorems
• Laws of logic

The undefined terms or primitive terms of geometry are points, lines and planes that at some point meet or join together. This is called incidence, since geometry studies their relationship. E.g. 3 lines that form a triangle on a plane.