This document discusses the structure of an axiomatic system in mathematics. An axiomatic system consists of undefined terms, defined terms, axioms or postulates, and theorems. Axioms or postulates are statements that are assumed to be true without proof, while theorems are statements that need to be proven using the axioms and previously proven theorems. The document also defines an axiomatic system as a set of axioms used to derive theorems in order to develop and prove statements in a field of mathematics like geometry.

1. AXIOMATIC
STRUCTURE OF
GEOMETRY

2. MATHEMATICAL
SYSTEM
UNDEFINED TERMS 1

3. MATHEMATICAL
SYSTEM
UNDEFINED TERMS 1
DEFINED TERMS 2

4. MATHEMATICAL
SYSTEM
UNDEFINED TERMS 1
DEFINED TERMS 2
AXIOMS/POSTULATES 3

5. MATHEMATICAL
SYSTEM
Which of the following is true
about axioms/postulates?
A. It is a statement that needs to be proven.
B. It is a statement that is assumed to be true
even without proof.
C. It is a statement that shows the meaning of a
certain term in mathematics.

6. MATHEMATICAL
SYSTEM
UNDEFINED TERMS 1
DEFINED TERMS 2
AXIOMS/POSTULATES 3
THEOREMS 4

7. MATHEMATICAL
SYSTEM
Which of the following is true
about theorems?
A. It is a statement that needs to be proven.
B. It is a statement that is assumed to be true
even without proof.
C. It is a statement that shows the meaning of a
certain term in mathematics.

8. Learning
Objectives

9. Subtasks:
1. define axiomatic system;
2. determine the importance of an
axiomatic system in geometry

10. What is AXIOMATIC SYSTEM?
Axiomatic system
refers to the
statements and rules
used to develop and
prove theorems.
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11. What is AXIOMATIC SYSTEM?
 is a set of axioms
used to derive
theorems.
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you
Mirjam Nilsson
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