Lesson plan in geometry

GEOMETRYINTRODUCTIONLOGICAL REASONING

Lesson Plan of:Lorena M. Masbaño

GEOMETRY

GEOMETRY

GEOMETRY

GEOMETRYcomes from the two Greek words:

Geo - “earth”Metri-“Measurement”.

GEOMETRY

deals with shapes that we see in the world each day

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

Elementsthis is the book of Euclid which contains the fundamentals and concepts 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?

RH BILL

RH BILL

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

RH BILL

2. What do you know about the said issue?

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?

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

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

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

qp

EXAMPLE 1:Glass objects are fragile.

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

LOGICAL REASONING

Converse Statement:

-“If q, then p” is written as pq

EXAMPLE 1:Glass objects are fragile.

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

LOGICAL REASONING

Inverse Statement:

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

EXAMPLE 1:Glass objects are fragile.

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

LOGICAL REASONING

Contrapositive Statement:

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

pq ~~

EXAMPLE 1:Glass objects are fragile.

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

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

EXAMPLE 1:Glass objects are fragile.

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

For BICONDITIONAL:ORIGINAL: Mammals have mammary glands

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

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)

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

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.

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.

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

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

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

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

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

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

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”

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

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.

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.

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

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

Conclusion: ∟1 and ∟2 are congruent.

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.

INDUCTIVE REASONING:

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

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

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

Using inductive reasoning to make a generalization called conjecture.

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

THE END