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Elements this is the book of Euclid which contains the fundamentals and concepts in Geometry.
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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?
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RH BILL1. Who among you have heard or read anything about the issue on RH Bill?
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RH BILL2. What do you know about the said issue?
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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?
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Every time we expressed an argument, we used statements that would really hit the idea that we want to express.
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That is why we need to think carefully and logically so that the statement would be accepted as true.
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LOGICAL REASONINGConditional Statement p q has two parts: a hypothesis denoted by p, and a conclusion, denoted by q.
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EXAMPLE 1:Glass objects are fragile.Conditional:If the objects are made of glass, then they are fragile. (TRUE)
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LOGICAL REASONINGConverse Statement:-“If q, then p” is written as q p
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EXAMPLE 1:Glass objects are fragile.Converse:If the objects are fragile, then they are made of glass. (FALSE)
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LOGICAL REASONINGInverse Statement:- “If not p, then not q” is written as ~ p ~ q
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EXAMPLE 1:Glass objects are fragile.Inverse:If the objects are not made of glass, then they are not fragile. (FALSE)
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LOGICAL REASONINGContrapositive Statement:- “If not q, then not p” is written as ~ q ~ p
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EXAMPLE 1:Glass objects are fragile.Contrapositive:If the objects are not fragile, then they are not made of glass. (FALSE)
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LOGICAL REASONINGBiconditional:is form when a conditional and its converse are both true.In symbols: “p if and only if q” is written as p q
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EXAMPLE 1:Glass objects are fragile.Biconditional:No biconditional statements can be drawn since the converse statement is false.
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For BICONDITIONAL:ORIGINAL: Mammals have mammary glandsCONDITIONAL: If an animal is a mammal, then it has a mammary gland. (TRUE)
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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)
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Conditional statement may be true or false. To show that a conditional statement is TRUE, you must construct a logical argument using reasons.
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1. Definition- a statement of a word, or term, or phrase which made use of previously defined terms2. Postulate- is a statement which is accepted as true without proof.
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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.
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EXAMPLE 2:Complementary angles are any twoangles whose sum of their measureis 90.CONDITIONAL: If two angles are complementary, then the sum of their measure is 90 . TRUE
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CONVERSE: If the sum of the measures of two angles is 90, then they are complementary. TRUEBICONDITIONAL: Two angles are complementary if and only if the sum of their measure is 90. TRUE
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INVERSE: If two angles are not complementary, then the sum is not . TRUECONTRAPOSITIVE: If the sum of the measures of two angles is not 90, then they are not complementary. TRUE
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EXAMPLE 3:The sum of two odd numbers iseven.CONDITIONAL: If two numbers are odd, then their sum is even. TRUECONVERSE: If the sum of two numbers is even, then they are odd numbers. TRUE
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BICONDITIONAL: Two numbers are odd if and only if their sum is even. TRUEINVERSE: If two numbers are even, then their sum is odd. FALSE
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CONTRAPOSITIVE: If the sum of the numbers is odd, then they are odd numbers. FALSE
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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”
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SYLLOGISM- an argument made up of three statements: a major premise, a minor premise (both of which are accepted as true), and a conclusion.
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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.
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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.
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EXAMPLES OF SYLLOGISM:Major Premise: Right angles are congruent.Minor Premise: ∟1 and ∟2 are right angles.Conclusion: ∟1 and ∟2 are congruent.
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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.
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INDUCTIVE REASONING:It is a process of observing data, recognizing patterns, and making generalizations from observations.
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Geometry is rooted in inductive reasoning. The geometry of ancient times was a collection of procedures and measurements that gave answers to practical problems.
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Used to calculate land areas, build canals, and build pyramids.Using inductive reasoning to make a generalization called conjecture.
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Use inductive reasoning to find thenext term/figure of each sequence.
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