Geometry 2-2 Conditional, Converse, Inverse,

Contrapositive Statements

Learning Targets• Students will be able to…

o Write the inverse, converse, and contrapositive of a conditional statement.

o Identify, write and analyze the true of conditional statements

Warm-up1. Find midpoint B of . The coordinates of endpoint A are (-5, 7) and the coordinates of endpoint C is(2, 8).  2. Find AC given the coordinates above.

Go over TestGo over Chapter 1 Test

Pass back homework packets with current grades.

Vocabulary OverviewWe will be looking at 4 key vocabulary words today.

Conditional StatementsConverse StatementsInverse StatementsContrapositive Statements.

Conditional StatementConditional Statement:

• When the statement is written in if-then form, the “if” part contains the hypothesis and the “then” part contains the conclusion.

A statement that can be written in the form if… then …

Think of the hypothesis as p and the conclusion as q.

If p then qp q

• Example:

If it is Friday then Mrs. Killam will wear a wolf shirt.

*Your turn! Make up an if then statement (conditional statement) and then find the hypothesis and the conclusion.

hypothesis conclusion

Deciding if true!• Not all conditional, converse, contrapositive, or

inverse statements will be true.

• A statement might be true for one and not the others.

• It is a possibility for them all to be true!

Converse StatementsConverse Statement

Statement formed by exchanging the hypothesis and conclusion.

q p

Converse Statement Examples

Example 1:

Statement: If you see lightning, then you hear thunder. Converse:

If you hear thunder, then you see lightning.

Converse Statement Examples

Example 2:Statement: If 2 segments are congruent, then they have the same length.

Converse:

If 2 segments have the same length, then they are congruent.

Make sure that you include the subject in the if part so that you know what you are talking about. Don’t just flip the two pieces.

What is a negation?• The negation of a statement is writing the

negative of the statement.

• Example:

Statement Negation

Angle A is acute

°

Angle A is not acute

This will be important when you are finding the Inverse and Contrapositive Statements!

Inverse StatementWhen you negate a conditional statement, you form the inverse.

Ex: Conditional: If it is raining, then it is cloudy.

Inverse:

If it is not raining, then it is not cloudy.

~p ~q ~ means not

Contrapositive Statement

When you negate a converse statement, you form the contrapositive.

Ex: Converse: If you hear thunder, then you see lightning. Contrapositive:

If you do not hear thunder, then you do not see lightning.

~q ~p

Putting it all togetherConditional Statement:

Inverse:

Converse:

Contrapositive

If the temperature is warm, then you can play outside.

If the temperature is not warm, then you cannot play outside.

If you can play outside, then the temperature is warm.

If you cannot play outside, then the temperature is not warm.

Can it be true??Conditional Statement:

Inverse:

Converse:

Contrapositive

If the temperature is warm, then you can play outside.

Is this true???If the temperature is not warm, then you cannot play outside.

Is this true???

If you can play outside, then the temperature is warm.

Is this true???

If you cannot play outside, then the temperature is not warm.

Is this true???

Putting it all togetherConditional Statement:

Inverse:

Converse:

Contrapositive

If the then angle A is acute.

If , then angle A is not acute.

If angle A is acute, then .

If angle A is not acute, then .

Can it be true?Conditional Statement:

Inverse:

Converse:

Contrapositive

If the then angle A is acute.Is this true???

If , then angle A is not acute.Is this true???

If angle A is acute, then .Is this true???

If angle A is not acute, then .Is this true???

Be careful with the NOTs

Conditional Statement:

Inverse:

Converse:

Contrapositive

If there is snow on the ground, then the flowers are not in bloom.

If there is not snow on the ground, then the flowers are in bloom.

If flowers are not in bloom, then there is snow on the ground.

If flowers are in bloom, then there is not snow on the ground.

Be careful with the NOTs

Conditional Statement:

Inverse:

Converse:

Contrapositive

If there is snow on the ground, then the flowers are not in bloom.

Is this true???If there is not snow on the ground, then the flowers are in bloom.

Is this true???

If flowers are not in bloom, then there is snow on the ground.

Is this true???

If flowers are in bloom, then there is not snow on the ground.

Is this true???

Advertisement ProjectHERE IS WHAT YOU NEED TO DO: (See example below)

Use the back side of this page for your work.1. Choose two advertisements out of a magazine. 2. Carefully rip them out, and attach them to another piece of paper.3. Write the advertisement as a conditional statement.4. Underline the hypothesis; Circle the conclusion.5. Write the converse, inverse and contrapositive.6. Are the converse, inverse and contrapositive true statements? Be sure to explain why.

Advertisement ProjectExample: Neutrogena Advertisement Conditional Statement: If you use Neutrogena, then you will clear blemishes and prevent breakouts. Converse Statement: If you clear blemishes and prevent breakouts, then you use Neutrogena. This is not true, because I could be using another skin product. Inverse Statement: If you do not use Neutrogena, then you will not clear blemishes and prevent breakouts. This is not true you could not use Neutrogena and still have clear skin. Contrapositive Statement: If you don’t clear blemishes and prevent breakouts, then you don’t use Neutrogena. This is true, because if you did, you would be clearing blemishes.

Advertisement ProjectHere is how you will be scored:Conditional Statement: 2 pointsConverse and explanation: 4 pointsInverse and explanation 4 pointsContrapositive and explanation: 4 points

Total 14 points x 2 articles = 28

points

Advertisement ProjectPlease fill find your advertisements first

Then fill out the back sheet of this paper and have it checked before writing on your construction paper!

Show examples of student work! Do not copy!