49
GEOMETRY INTRODUCTION LOGICAL REASONING Lesson Plan of: Lorena M. Masbaño

Lesson plan in geometry

Embed Size (px)

DESCRIPTION

The Power point presentation in Logical Reasoning

Citation preview

Page 1: Lesson plan in geometry

GEOMETRYINTRODUCTIONLOGICAL REASONING

Lesson Plan of:Lorena M. Masbaño

Page 2: Lesson plan in geometry

GEOMETRY

Page 3: Lesson plan in geometry

GEOMETRY

Page 4: Lesson plan in geometry

GEOMETRY

Page 5: Lesson plan in geometry

GEOMETRYcomes from the two Greek words:

Geo - “earth”Metri-“Measurement”.

Page 6: Lesson plan in geometry

GEOMETRY

deals with shapes that we see in the world each day

Page 7: Lesson plan in geometry

EuclidAn ancient Greek philosopher who first developed Geometry around 300 B.C.

Page 8: Lesson plan in geometry

Elementsthis is the book of Euclid which contains the fundamentals and concepts in Geometry.

Page 9: Lesson plan in geometry

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?

Page 10: Lesson plan in geometry

RH BILL

Page 11: Lesson plan in geometry

RH BILL

1. Who among you have heard or read anything about the issue on RH Bill?

Page 12: Lesson plan in geometry

RH BILL

2. What do you know about the said issue?

Page 13: Lesson plan in geometry

RH BILL3. What is your stand about the Bill? Are you pro-RH Bill? Or are you against it?

4. Why do you say so?

Page 14: Lesson plan in geometry

Every time we expressed an argument, we used statements that would really hit the idea that we want to express.

Page 15: Lesson plan in geometry

That is why we need to think carefully and logically so that the statement would be accepted as true.

Page 16: Lesson plan in geometry

LOGICAL REASONINGConditional Statement has two parts: a hypothesis denoted by p, and a conclusion, denoted by q.

qp

Page 17: Lesson plan in geometry

EXAMPLE 1:Glass objects are fragile.

Conditional: If the objects are made of glass, then they are fragile. (TRUE)

Page 18: Lesson plan in geometry

LOGICAL REASONING

Converse Statement:

-“If q, then p” is written as pq

Page 19: Lesson plan in geometry

EXAMPLE 1:Glass objects are fragile.

Converse: If the objects are fragile, then they are made of glass. (FALSE)

Page 20: Lesson plan in geometry

LOGICAL REASONING

Inverse Statement:

- “If not p, then not q” is written as qp ~~

Page 21: Lesson plan in geometry

EXAMPLE 1:Glass objects are fragile.

Inverse: If the objects are not made of glass, then they are not fragile. (FALSE)

Page 22: Lesson plan in geometry

LOGICAL REASONING

Contrapositive Statement:

- “If not q, then not p” is written as

pq ~~

Page 23: Lesson plan in geometry

EXAMPLE 1:Glass objects are fragile.

Contrapositive:If the objects are not fragile, then they are not made of glass. (FALSE)

Page 24: Lesson plan in geometry

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 qp

Page 25: Lesson plan in geometry

EXAMPLE 1:Glass objects are fragile.

Biconditional: No biconditional statements can be drawn since the converse statement is false.

Page 26: Lesson plan in geometry

For BICONDITIONAL:ORIGINAL: Mammals have mammary glands

CONDITIONAL: If an animal is a mammal, then it has a mammary gland. (TRUE)

Page 27: Lesson plan in geometry

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)

Page 28: Lesson plan in geometry

Conditional statement may be true or false. To show that a conditional statement is TRUE, you must construct a logical argument using reasons.

Page 29: Lesson plan in geometry

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.

Page 30: Lesson plan in geometry

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.

Page 31: Lesson plan in geometry

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

Page 32: Lesson plan in geometry

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

Page 33: Lesson plan in geometry

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

Page 34: Lesson plan in geometry

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

Page 35: Lesson plan in geometry

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

Page 36: Lesson plan in geometry

CONTRAPOSITIVE: If the sum of the numbers is odd, then they are odd numbers. FALSE

Page 37: Lesson plan in geometry

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”

Page 38: Lesson plan in geometry

SYLLOGISM- an argument made up of three statements: a major premise, a minor premise (both of which are accepted as true), and a conclusion.

Page 39: Lesson plan in geometry

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.

Page 40: Lesson plan in geometry

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.

Page 41: Lesson plan in geometry

EXAMPLES OF SYLLOGISM:Major Premise: Right angles are congruent.

Minor Premise: ∟1 and ∟2 are right angles.

Conclusion: ∟1 and ∟2 are congruent.

Page 42: Lesson plan in geometry

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.

Page 43: Lesson plan in geometry

INDUCTIVE REASONING:

It is a process of observing data, recognizing patterns, and making generalizations from observations.

Page 44: Lesson plan in geometry

Geometry is rooted in inductive reasoning. The geometry of ancient times was a collection of procedures and measurements that gave answers to practical problems.

Page 45: Lesson plan in geometry

Used to calculate land areas, build canals, and build pyramids.

Using inductive reasoning to make a generalization called conjecture.

Page 46: Lesson plan in geometry

Use inductive reasoning to find the next term/figure of each sequence.

Page 47: Lesson plan in geometry
Page 48: Lesson plan in geometry
Page 49: Lesson plan in geometry

THE END