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# Math 1 February 7 th - PowerPoint PPT Presentation

Math 1 February 7 th. 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.

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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.

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.

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.

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

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

How do I recognize and analyze a conditional statement?

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”

Example:

(Original) I breathe when I sleep

(Conditional) If I am sleeping, then I am

breathing.

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

Converse

Inverse

Contrapositive

• 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.

• 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.

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.

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

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.

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

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

They are both true.

They are logically equivalent.

The inverse and the converse have the same truth value.

They are both false.

They are logically equivalent.

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”

• hypothesis

• Conclusion

• neither

• hypothesis

• Conclusion

• neither

• hypothesis

• Conclusion

• neither

• 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.

• 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)