hypothesis conclusion (geometry 1_4)

Conditional Statements and Their ConversesConditional Statements and Their Converses

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

You will learn to write statements in if-then form and writethe converse of the statements.

Conditional Statements and Their ConversesConditional Statements and Their Converses

Conditional statements have two parts.

The part following if is the _________ .hypothesis

The part following then is the _________ .conclusion

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

Hypothesis:

Conclusion:

Conditional Statements and Their ConversesConditional Statements and Their Converses

Conditional statements have two parts.

The part following if is the _________ .hypothesis

The 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:

Conditional Statements and Their ConversesConditional Statements and Their Converses

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.

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

Conditional Statements and Their ConversesConditional Statements and Their Converses

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.

Conditional Statements and Their ConversesConditional Statements and Their Converses

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 givingone counterexample.

Whales live in water, butwhales are mammals, not fish.

Conditional Statements and Their ConversesConditional Statements and Their Converses

There are different ways to express a conditional statement.The following statements all have the same meaning.

If you are a member of Congress, then you are a U.S. citizen.

All members of Congress are U.S. citizens.

You are a U.S. citizen if you are a member of Congress.

Conditional Statements and Their ConversesConditional Statements and Their Converses

There are different ways to express a conditional statement.The following statements all have the same meaning.

If you are a member of Congress, then you are a U.S. citizen.

All members of Congress are U.S. citizens.

You are a U.S. citizen if you are a member of Congress.

You write two other forms of this statement: “If two lines are parallel, then they never intersect.”

Conditional Statements and Their ConversesConditional Statements and Their Converses

There are different ways to express a conditional statement.The following statements all have the same meaning.

If you are a member of Congress, then you are a U.S. citizen.

All members of Congress are U.S. citizens.

You are a U.S. citizen if you are a member of Congress.

You write two other forms of this statement: “If two lines are parallel, then they never intersect.”

All parallel lines never intersect.

Lines never intersect if they are parallel.

Possible answers:

Conditional Statements and Their ConversesConditional Statements and Their Converses

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

converse

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

Converse: If _______________, then ________________.

Conditional Statements and Their ConversesConditional Statements and Their Converses

The ________ of a conditional statement if 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 ________________.

Conditional Statements and Their ConversesConditional Statements and Their Converses

The ________ of a conditional statement if 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 triangle it has three angles

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

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

Conditional Statements and Their ConversesConditional Statements and Their Converses

The ________ of a conditional statement if 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 triangle it has three angles

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.

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

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.”

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

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

TRUE!

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.

TRUE!

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!

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!

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.

Conditional Statements and Their ConversesConditional Statements and Their Converses