Conditional Statements 9.3.2.2 Accurately interpret and use words and phrases in geometric proofs...

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Conditional Statements 9.3.2.2 Accurately interpret and use words and phrases in geometric proofs such as "if…then," "if and only if," "all," and "not." Recognize the logical relationships between an "if…then" statement and its inverse, converse and contrapositive.

Transcript of Conditional Statements 9.3.2.2 Accurately interpret and use words and phrases in geometric proofs...

Page 1: Conditional Statements 9.3.2.2 Accurately interpret and use words and phrases in geometric proofs such as "if…then," "if and only if," "all," and "not."

Conditional Statements

9.3.2.2 Accurately interpret and use words and phrases in geometric proofs such as "if…then," "if and only if," "all," and "not." Recognize the logical relationships between an "if…then" statement and

its inverse, converse and contrapositive.

Page 2: Conditional Statements 9.3.2.2 Accurately interpret and use words and phrases in geometric proofs such as "if…then," "if and only if," "all," and "not."

Guiding Question: Why should we have logical arguments?

O Lesson Objective: I will be able to write a conditional statement and its converse

O Logical arguments in mathematics are the basis for proof.

O This translates into scientific research as all theories in science and math need to be based on given data and research.

Page 3: Conditional Statements 9.3.2.2 Accurately interpret and use words and phrases in geometric proofs such as "if…then," "if and only if," "all," and "not."

Guiding Question: Why should we have logical arguments?

How some students see math problems…

Conditional Statement

O A statement made in 2 parts using “if-then” form.

O General Form: if (hypothesis) then (conclusion)

O If p then q

Page 4: Conditional Statements 9.3.2.2 Accurately interpret and use words and phrases in geometric proofs such as "if…then," "if and only if," "all," and "not."

Guiding Question: Why should we have logical arguments?

Convert these into conditional (if-then) statements1. All chickens lay

eggs.2. My uncle is tall.3. Central is my

high school.4. Hamburgers

are good.

O If _____, then ______

Page 5: Conditional Statements 9.3.2.2 Accurately interpret and use words and phrases in geometric proofs such as "if…then," "if and only if," "all," and "not."

Guiding Question: Why should we have logical arguments?

O The converse of a statement means to switch around the hypothesis and the conclusion

O Conditional StatementO If p, then q

O Converse of ConditionalO If q, then p

O Write the converse of these.

1. If I am cold, then I put on a sweatshirt.

2. If there are clouds, it is cold.

3. If lunch is fish, then I won’t eat lunch.

Page 6: Conditional Statements 9.3.2.2 Accurately interpret and use words and phrases in geometric proofs such as "if…then," "if and only if," "all," and "not."

Guiding Question: Why should we have logical arguments?

O Convert these to conditional statements and then find the converse statements

1. When I am hungry I eat.2. A frog is green.3. Bears hibernate in the winter.4. Seniors are older then

freshmen.

Page 7: Conditional Statements 9.3.2.2 Accurately interpret and use words and phrases in geometric proofs such as "if…then," "if and only if," "all," and "not."

Guiding Question: Why should we have logical arguments?

O Assignment: Conditional and Converse WS.


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