Lesson plan in geometry
Download as PPTX, PDF2 likes3,084 views
This document discusses logical reasoning and different types of logical statements. It provides examples of conditional, converse, inverse, and contrapositive statements. A conditional statement relates a hypothesis and conclusion, and may be true or false. The document also discusses deductive reasoning using syllogisms as examples, and inductive reasoning which makes generalizations from observations.
Lesson plan in geometry
- 1. INTRODUCTION LOGICAL REASONING Lesson Plan of: Lorena M. Masbaño
- 2. GEOMETRY
- 3. GEOMETRY
- 4. GEOMETRY
- 5. GEOMETRY comes from the two Greek words: Geo - “earth” Metri-“Measurement”.
- 6. GEOMETRY deals with shapes that we see in the world each day
- 8. Elements this is the book of Euclid which contains the fundamentals and concepts in Geometry.
- 9. Thoughts to ponder: What do you think will happen if Geometry was not discovered or introduced to the World? •What would its effects to the infrastructure? to houses? to businesses?
- 10. RH BILL
- 11. RH BILL 1. Who among you have heard or read anything about the issue on RH Bill?
- 12. RH BILL 2. What do you know about the said issue?
- 13. RH BILL 3. What is your stand about the Bill? Are you pro-RH Bill? Or are you against it? 4. Why do you say so?
- 14. Every time we expressed an argument, we used statements that would really hit the idea that we want to express.
- 15. That is why we need to think carefully and logically so that the statement would be accepted as true.
- 16. LOGICAL REASONING Conditional Statement p q has two parts: a hypothesis denoted by p, and a conclusion, denoted by q.
- 17. EXAMPLE 1: Glass objects are fragile. Conditional: If the objects are made of glass, then they are fragile. (TRUE)
- 18. LOGICAL REASONING Converse Statement: -“If q, then p” is written as q p
- 19. EXAMPLE 1: Glass objects are fragile. Converse: If the objects are fragile, then they are made of glass. (FALSE)
- 20. LOGICAL REASONING Inverse Statement: - “If not p, then not q” is written as ~ p ~ q
- 21. EXAMPLE 1: Glass objects are fragile. Inverse: If the objects are not made of glass, then they are not fragile. (FALSE)
- 22. LOGICAL REASONING Contrapositive Statement: - “If not q, then not p” is written as ~ q ~ p
- 23. EXAMPLE 1: Glass objects are fragile. Contrapositive: If the objects are not fragile, then they are not made of glass. (FALSE)
- 24. LOGICAL REASONING Biconditional: is form when a conditional and its converse are both true. In symbols: “p if and only if q” is written as p q
- 25. EXAMPLE 1: Glass objects are fragile. Biconditional: No biconditional statements can be drawn since the converse statement is false.
- 26. For BICONDITIONAL: ORIGINAL: Mammals have mammary glands CONDITIONAL: If an animal is a mammal, then it has a mammary gland. (TRUE)
- 27. For BICONDITIONAL: CONVERSE: If an animal has mammary gland, then it is a mammal. (TRUE) BICONDITIONAL: An animal is a mammal if and only if it has a mammary gland. (TRUE)
- 28. Conditional statement may be true or false. To show that a conditional statement is TRUE, you must construct a logical argument using reasons.
- 29. 1. Definition- a statement of a word, or term, or phrase which made use of previously defined terms 2. Postulate- is a statement which is accepted as true without proof.
- 30. 3. Theorem- is any statement that can be proved true. 4. Corollary- to a theorem is a theorem that follows easily from a previously proved theorem.
- 31. EXAMPLE 2: Complementary angles are any two angles whose sum of their measure is 90. CONDITIONAL: If two angles are complementary, then the sum of their measure is 90 . TRUE
- 32. CONVERSE: If the sum of the measures of two angles is 90, then they are complementary. TRUE BICONDITIONAL: Two angles are complementary if and only if the sum of their measure is 90. TRUE
- 33. INVERSE: If two angles are not complementary, then the sum is not . TRUE CONTRAPOSITIVE: If the sum of the measures of two angles is not 90, then they are not complementary. TRUE
- 34. EXAMPLE 3: The sum of two odd numbers is even. CONDITIONAL: If two numbers are odd, then their sum is even. TRUE CONVERSE: If the sum of two numbers is even, then they are odd numbers. TRUE
- 35. BICONDITIONAL: Two numbers are odd if and only if their sum is even. TRUE INVERSE: If two numbers are even, then their sum is odd. FALSE
- 36. CONTRAPOSITIVE: If the sum of the numbers is odd, then they are odd numbers. FALSE
- 37. DEDUCTIVE REASONING -from deduce means to reason form known facts; -use in proving theorem; -using existing structures to deduce new parts of the structure. -“if a, then b”
- 38. SYLLOGISM - an argument made up of three statements: a major premise, a minor premise (both of which are accepted as true), and a conclusion.
- 39. EXAMPLES OF SYLLOGISM: Major Premise: If the numbers are odd, then their sum is even. Minor Premise: The numbers 3 and 5 are odd numbers. Conclusion: the sum of 3 and 5 is even.
- 40. EXAMPLES OF SYLLOGISM: Major Premise: If you want good health, then you should get 8 hours of sleep a day. Minor Premise: Aaron wants good health. Conclusion: Aaron should get 8 hours of sleep a day.
- 41. EXAMPLES OF SYLLOGISM: Major Premise: Right angles are congruent. Minor Premise: ∟1 and ∟2 are right angles. Conclusion: ∟1 and ∟2 are congruent.
- 42. EXAMPLES OF SYLLOGISM: Major Premise: Diligent students do their homeworks. Minor Premise: Amy and Andy are diligent students. Conclusion: Amy and Andy do their homeworks.
- 43. INDUCTIVE REASONING: It is a process of observing data, recognizing patterns, and making generalizations from observations.
- 44. Geometry is rooted in inductive reasoning. The geometry of ancient times was a collection of procedures and measurements that gave answers to practical problems.
- 45. Used to calculate land areas, build canals, and build pyramids. Using inductive reasoning to make a generalization called conjecture.
- 46. Use inductive reasoning to find the next term/figure of each sequence.
- 49. THE END