1. MATHEMATICAL SYSTEM

2. LEARNING OBJECTIVES: 1.DEFINE THE DIFFERENT TERMS IN THE MATHEMATICAL SYSTEM; 2.CONSTRUCT THE AXIOMATIC STRUCTURE; AND 3.DEMONSTRATE APPRECIATION OF MATHEMATICAL SYSTEM THROUGH ACTIVE PARTICIPATION AND COORDINATION WITH VARIED ACTIVITIES.

4. ACTIVITY 1: WORD JUMBLE 1.INLE 2.MXOIA 3.TIONP 4.ENPLA 5.YRA 6.ETALUTSOP 7.ELGNA 8.GESTNTME 9.MEROEHT 10.OXAIMCITA SEMTYS

5. Working on groups, you will define and make a schematic diagram given the following geometric terms according to your prior knowledge. Write it on a manila paper. You can use your phones for the definition. One representative of each group will present your output.

6. AXIOM/POSTULATE Axiom/postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.

7. AXIOM Axiom is any mathematical statement that serves as a starting point from which other statements are logically derived.

8. AXIOMATIC SYSTEM Axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems.

9. THEOREMS Theorem is a statement proven based on axioms, other theorems, and some set of logical connectives.

10. COROLLARY It is a theorem that is usually considered an easy consequence/result of another theorem.

11. LEMMA It is generally used to describe an auxiliary fact that is used in the proof of a more significant result.

12. UNDEFINED TERMS It is the terms that are not precisely defined and are generally accepted.

13. UNDEFINED TERMS It is the terms that are not precisely defined and are generally accepted.

14. UNDEFINED TERMS It is the terms that are not precisely defined and are generally accepted.

15. UNDEFINED TERMS It is the terms that are not precisely defined and are generally accepted.

16. DEFINED TERMS It is the terms that are defined using the undefined terms.

17. 4 CHARACTERICS OF A GOOD DEFINITION: 1.It names the term being defined. 2.It places the term into a set or category. 3.It distinguishes itself from other terms in that category (without providing unnecessary facts). 4.It is reversible. (ex. If a triangle is isosceles, then it has two congruent sides; if a triangle has two congruent sides, then it is isosceles.)

18. MATHEMATICAL SYSTEM UNDEFINED TERMS are terms that do not require a definition but can be described. These terms are used as a base to define other terms, hence, these are the building blocks of other mathematical terms, such as definitions, axioms, and theorems.

19. MATHEMATICAL SYSTEM DEFINED TERMS are the terms of mathematical system that can be defined using undefined terms. Term or phrase which makes use of the undefined terms and previously defined terms and common words.

20. MATHEMATICAL SYSTEM AXIOM/POSTULATES A statement which is accepted as true without proof. These statements can be used as reasons in proving some mathematical statements.

21. MATHEMATICAL SYSTEM THEOREMS Theorems are statements accepted after they are proven true deductively.

22. UNDEFINED TERMSDEFINED TERMSAXIOMS/POSTULATES THEOREMS POINT MATHEMATICAL SYSTEM LINE PLANE LINE SEGMENT RAY ANGLES POLYGONS AXIOMS POSTULATES THEOREMS

23. LINE LINE SEGMENT Two points determine a line The shortest segment from a point not on a line to the line is the perpendicular segment UNDEFINED TERMS DEFINED TERMS AXIOMS/POSTULATES THEOREMS

24. The axiomatic structure of a mathematical system follows a sequence, starting with a set of undefined terms which are bases to define terms, then axioms that are clearly stated, and from these a theorem is derived through reasoning. Theorems are derived from the set of axioms in an axiomatic mathematical system.

25. 1.What is axiomatic system? 2.What are the four main parts of mathematical system? 3.How are each related to each other? 4.What are the characteristics of the defined terms?

26. COLUMN ACOLUMN B ___1. Geometric terms which definitions are derived from the undefined terms. A. Undefined terms ___2. It is a statement proven based on axioms, other theorems, and some set of logical connectives. B. Defined terms ___3. It is a general statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. C. Axiom ___4. These are geometric terms that are not precisely defined but generally accepted. D. Postulate ___5. A statement which is accepted as true without proof. These statements can be used as reasons in proving some mathematical statements. E. Theorem

27. A sari – sari store owner bought five different brands of detergent powder namely,,,, and. He bought 20 pieces for each brand. Even at a glance, he can easily state which brand of detergent powder is the best seller. Now, each powder claims that it would not irritate the skin after using it. In this case, the store owner wants to test each brand to prove if the claim is true.

28. 1. What represents or describes the undefined terms in the situation? 2. What statement represents an axiom? Why? 3. What statement represents a theorem? Justify your answer. 4. How do this statement related to mathematical system?

29. Working by pair, remake the axiomatic structure using the following terms: Axiom, Postulate, Axiomatic System, Theorem, Defined Terms, Three Undefined Terms, Point, Plane, Five Postulates, Line.