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Math 1 February 7th

Turn in Homework – page 16

Warm Up

If it is Tuesday, then tomorrow is Wednesday.

What is the hypothesis?

What is the conclusion?

Write the contrapositive of this statement.

Check homework – page 16

a) If a triangle has a 90° angle, then it is a right triangle.

b) If a triangle is NOT a right triangle, then it does not have a 90° angle.

c) If a triangle does not have a 90° angle, then it is not have a right triangle.

Check homework – page 16

2. a) If a quadrilateral is not a rhombus, then it has exactly two congruent sides.

b) If a quadrilateral does not have exactly two congruent sides, then it is a rhombus

c) If a quadrilateral is a rhombus, then it does not have exactly two congruent sides.

Check homework – page 16

3. a) If two segments have the same length, then they are congruent.

b) If two segments are not congruent, then they do not have the same length.

c) If two segments do not have the same length, then they are not congruent.

Reasoning and Proof

2.1 Conditional Statements

In order to analyze statements, we will translate them into a logic statement called a conditional statement.

Essential Question:

How do I recognize and analyze a conditional statement?

2.1 Conditional Statements

conditional statement

- A _________________ is a statement that can be expressed in ________form.

“if-then”

2. A conditional statement has _________.

- The __________ is the ____ part.
- The __________ is the ______ part.

two parts

hypothesis

“if”

conclusion

“then”

2.1 Conditional Statements

Example:

(Original) I breathe when I sleep

(Conditional) If I am sleeping, then I am

breathing.

2.1 Conditional Statements

To fully analyze this conditional statement, we need to find three new conditionals:

Converse

Inverse

Contrapositive

2.1 Conditional Statements

- The ________ of a conditional statement is formed by switching the hypothesis and the conclusion.
- Example:

converse

(Conditional) If I am sleeping, then I am

breathing.

(Converse) If I am breathing, then I am sleeping.

2.1 Conditional Statements

- The ________ of a conditional statement is formed by negating (inserting “not”) the hypothesis and the conclusion.
- Example:

inverse

(Conditional) If I am sleeping, then I am

breathing.

(Inverse) If I am not sleeping, then

I am not breathing.

2.1 Conditional Statements

contrapositive

- The ______________ of a conditional statement is formed by negating the hypothesis and the conclusion of the converse.
- Example:
(Converse)If I am breathing, then I am sleeping.

(Contrapositive)If I am not breathing, then I am not sleeping.

2.1 Conditional Statements

If I am sleeping, then I am breathing.

if…then

If I am not sleeping, then I am not breathing.

insert not

If I am breathing, then I am sleeping.

switch

If I am not breathing, then I am not sleeping.

switch and insert not

2.1 Conditional Statements

The conditional statement, inverse, converse and contrapositive all have a truth value. That is, we can determine if they are true or false.

When two statements are both true or both false, we say that they are logically equivalent.

2.1 Conditional Statements

T

If m<A ≠ 30°, then <A is not acute.

F

If <A is acute, then

m<A = 30°.

F

If <A is not acute, then m<A ≠ 30°.

T

2.1 Conditional Statements

The conditional statement and its contrapositive have the same truth value.

They are both true.

They are logically equivalent.

2.1 Conditional Statements

The inverse and the converse have the same truth value.

They are both false.

They are logically equivalent.

Practice

Translate the following statement into a conditional statement. Then find the converse, inverse and contrapositive.

“A cloud of steam can be seen when the space shuttle is launched”

1. Identify the underlined portion of the conditional statement.

- hypothesis
- Conclusion
- neither

2. Identify the underlined portion of the conditional statement.

- hypothesis
- Conclusion
- neither

3. Identify the underlined portion of the conditional statement.

- hypothesis
- Conclusion
- neither

4. Identify the converse for the given conditional. statement.

- If you do not like tennis, then you do not play on the tennis team.
- If you play on the tennis team, then you like tennis.
- If you do not play on the tennis team, then you do not like tennis.
- You play tennis only if you like tennis.

5. Identify the inverse for the given conditional. statement.

- If 2x is not even, then x is not odd.
- If 2x is even, then x is odd.
- If x is even, then 2x is odd.
- If x is not odd, then 2x is not even.

HOMEWORK statement.

- Finish pages 18 and 19
- QUIZ ON THURSDAY!!!!! (Like page 19)

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