Students will analyze statements, write definitions as conditional statements and verify validity.Why? So you can verify statements, as seen in Ex 2.Mastery is 80% or better on 5-min checks and indy work.• “If I get straight A’s, then my

parents will buy me a car”

Key Vocabulary• Conditional Statement- page 79• If-then form – If Hypoth, then conclusion• Hypothesis- page 79• Conclusion- page 79• Negation- Opposite of original statement.• Converse- If C then H• Inverse – If not H then not C• Contrapositive- If not C then not H• Equivalent statements- Both true or both false• Perpendicular lines- two line intersect at a right

angle• Biconditional statement- If and only if…when

conditional and converse are true statements

In mathematics, you will come across many _______________.

For Example: If a number is even,

then it is divisible by two.

If – then statements join two statements based on a condition:

A number is divisible by two only if the number is even.

Therefore, if – then statements are also called ________ _______ .

if-then statements

conditional statements

Conditional Statements---Skill Develop Conditional Statements---Skill Develop

Conditional Statements and Their Converses Skill DevelopConditional Statements and Their Converses Skill Develop

Conditional statements have two parts.

The part following if is the _________ .hypothesisThe part following then is the _________ .conclusion

If a number is even, then the number is divisible by two.

a number is even

the number is divisible by two.

Hypothesis:

Conclusion:

Pair Share: Guided

What about?

If__________________________, then_________________________

If__________________________, then_________________________If it is a vertebrate, then it has a backbone.

If X equals 2, then X² equals 4

Conditional Statements and Their Converses GuidedConditional Statements and Their Converses Guided

How do you determine whether a conditional statement is true or false?

ConditionalStatement

True orFalse

Why?

If it is the 4th of July(in the U.S.), then it is aholiday.

True The statement is true becausethe conclusion follows fromthe hypothesis.

If an animal lives in the water, then it is a fish.

False You can show that the statement is false by givingA counter exampleone counterexampleWhales live in water, butwhales are mammals, not fish.

Conditional Statements and Their Converses GuidedConditional Statements and Their Converses Guided

In your notes determine whether each conditional statement is true or false?

ConditionalStatement

True orFalse

Why?

If you were on the BCHS varsity football team last year, then you were a league champion.

If Kobe Bryant scores 40+ points, then the Lakers win.

True

False

The statement is true becausethe conclusion follows fromthe hypothesis.

You can show that the statement is false by givingone counterexample.

Kobe could score 40+ and the Lakers could lose.

Conditional Statements and Their Converses GuidedConditional Statements and Their Converses Guided

The ________ of a conditional statement is formed by exchanging the hypothesis and the conclusion.

converse

Conditional: If a figure is a triangle, then it has three angles.

a figure is a triangleit has three anglesConverse: If _______________, then _________.

NOTE: You often have to change the wording slightly so that the converse reads smoothly.

Converse: If the figure has three angles, then it is a triangle.

• Negate the hypothesis & conclusion of a conditional statement.

• Ex: Write the inverse of “If you are a brunette, then you have brown hair.”

If you are not a brunette, then you do not

have brown hair.

To write an Inverse Skill DevelopTo write an Inverse Skill Develop

• Negate, then switch the hypothesis & conclusion of a conditional statement.

• Ex: Write the contrapositive of “If you are a brunette, then you have brown hair.”

If you do not have brown hair, then you are not a brunette.

To write a Contrapositive Skill DevelopTo write a Contrapositive Skill Develop

Think…Ink…Share Conditional Statements and Their Think…Ink…Share Conditional Statements and Their ConversesConverses

Think…..Ink…..Share

Survey Says…..

If- Then If an animal is a chimpanzee, then it loves bananas

Converse If an animal loves bananas then it is a chimpanzee.

Inverse If an animal is not a chimpanzee, then it does not love bananas

Contrapositive If an animal does not love bananas then it is not a chimpanzee.

If points are collinear, then they lie on the same line.

If points lie on the same line, then they are collinear

If points do not lie on the same line, then they not collinear.

If- Then

Converse

Inverse

Contrapositive

If points are not collinear, then they do not lie on the same line.

Complete the Following--CFU

Conditional Statements and Their ConversesConditional Statements and Their Converses

Write the converse of the following statements.State whether the converse is TRUE or FALSE.If FALSE, give a counterexample:

“If you are at least 16 years old, then you can get a driver’s license.”

If _______________________, then _______________________.you can get a driver’s license you are at least 16 years old

“If today is Saturday, then there is no school.

If _______________, then ______________.there is no school today is Saturday

TRUE!

FALSE!

We don’t have school on New Years day which may fall on a Monday.

right

right

Conditional Statements & Definitions Guided Conditional Statements & Definitions Guided

trueright

perpendicular

linear pairadjacent

false

Conditional Statements Conditional Statements Conditional Statements & Definitions Think……Ink……Share Conditional Statements & Definitions Think……Ink……Share

Conditional Statements & Definitions Conditional Statements & Definitions

How will we use these definitions?

Performance Task

What was the Objective?

• Students will analyze statements, write definitions as conditional statements and verify validity.

• Why? So you can verify statements, as seen in Ex 2.

• Mastery is 80% or better on 5-min checks and indy work.

Homework

• Students will write and test validity of conditional statements and their converses.

Pages 83-84•#2-28 Even