The-mathematical-system-Grade-8...........

Math Grade 8

1. riddle When does 9 + 5 = 2? 1

2. What do you see on the picture? What branch of mathematics do we cover these topics? 2

3. GEOMETRY - is  a branch of mathematics that studies the sizes, shapes, positions, angles, and dimensions of things

4. The mathematical system (axiomatic system) Mathematics 8 3 rd Quarter

5. Mathematical system (axiomatic system) Is set of axioms from which some or all axioms can be used in conjunction to logically derive theorems It is a system made up of undefined terms, defined terms, axioms/postulates, and theorems which are used in proving logical conclusions in geometry.

6. 6 Synergize scalable e-commerce Disseminate standardized metrics

7. UNDEFINED TERMS = terms that are not precisely defined and are generally accepted. Ex. Line, points, plane DEFINED TERMS = Terms that are defined using the undefined terms. Ex. Line segment, angle, polygons, etc. 4 CHARACTERICS OF A GOOD DEFINITION: It names the term being defined. It places the term into a set or category. It is distinguishes itself from other terms in that category (without providing unnecessary facts) It is reversible ( eg. If a triangle is isosceles, then it has two congruent sides ---> If a triangle has two congruent sides, then it is isosceles.) AXIOM / POSTULATE = is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. THEOREM = is a statement proven based on axioms, other theorems, and some set of logical connectives. 7

8. Presentation title 8

9. Assessment: 1) What do you call the statements that are assumed to be true and do not need proof? A. axioms B. defined terms C. theorems D. undefined terms 2) There are four parts of the Mathematical system. Which of the following is not a part of the mathematical system? A. corollary B. theorems C. axioms or postulate D. defined and undefined terms

10. Assessment: 3) Which of the following statements is true about axioms or postulates? 4) Which of the following statements is true about a postulate? A. It is never accepted to be true. B. It is accepted as true without a formal proof. C. It is only accepted as true after being formally proven. D. It is usually not obvious as true, so it must be proven. A. These are concepts that need to be defined. B. These are statements accepted after it is proved deductively. C. These are concepts that can be defined using the undefined terms. D. These are statements assumed to be true and need no further proof.

11. Assessment: 5) Which of the following best describes a theorem? A. It is the same thing as a postulate. B. It is a statement that is accepted as true without a formal proof. C. It is a statement that is impossible to be proven by mathematical reasoning. D. It is a statement that has been formally proven using mathematical reasoning. 6) What do you call the statements that can only be described and not defined? A. axioms C. theorems B. defined terms D. undefined terms

12. Assessment: 7) Baguio City is the summer capital of the Philippines. Which of the following best describes the statement? A. The statement is obviously false. B. The statement cannot be proven to be true or false. C. The statement needs to be formally proven to be accepted as true. D. The statement does not need to be formally proven and is accepted as true