Conditional, Converse, Inverse, Contrapositive Statements

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Conditional, Converse, Inverse, Contrapositive Statements Geometry 2-2 Conditional, Converse, Inverse, Contrapositive Statements

Learning Targets Students will be able to… Write the inverse, converse, and contrapositive of a conditional statement. Identify, write and analyze the true of conditional statements

Warm-up 1. Find midpoint B of 𝐴𝐶 . 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 Test Go over Chapter 1 Test Pass back homework packets with current grades.

Vocabulary Overview We will be looking at 4 key vocabulary words today. Conditional Statements Converse Statements Inverse Statements Contrapositive Statements.

Conditional 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 q p  q

If it is Friday then Mrs. Killam will wear a wolf shirt. 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 Statements Converse Statement Statement formed by exchanging the hypothesis and conclusion. q  p

Converse Statement Examples 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? Statement Negation 𝑚∠𝑎=30° Angle A is acute The negation of a statement is writing the negative of the statement. Example: Statement Negation 𝑚∠𝑎=30° Angle A is acute 𝑚∠𝑎≠30° Angle A is not acute This will be important when you are finding the Inverse and Contrapositive Statements!

Inverse Statement When you negate a conditional statement, you form the inverse. Ex: Conditional: If it is raining, then it is cloudy. Inverse: ~p  ~q ~ means not If it is not raining, then it is not cloudy.

Contrapositive Statement When you negate a converse statement, you form the contrapositive. Ex: Converse: If you hear thunder, then you see lightning. Contrapositive: ~q  ~p If you do not hear thunder, then you do not see lightning.

Putting it all together Conditional 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 together Conditional Statement: Inverse: Converse: Contrapositive If the 𝑚∠𝑎=30° then angle A is acute. If 𝑚∠𝑎≠30°, then angle A is not acute. If angle A is acute, then 𝑚∠𝑎=30°. If angle A is not acute, then 𝑚∠𝑎≠30°.

Can it be true? Conditional Statement: Inverse: Converse: Contrapositive If the 𝑚∠𝑎=30° then angle A is acute. Is this true??? If 𝑚∠𝑎≠30°, then angle A is not acute. Is this true??? If angle A is acute, then 𝑚∠𝑎=30°. Is this true??? If angle A is not acute, then 𝑚∠𝑎≠30°. 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 Project HERE 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 Project Example: 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 Project Here is how you will be scored: Conditional Statement: 2 points Converse and explanation: 4 points Inverse and explanation 4 points Contrapositive and explanation: 4 points Total 14 points x 2 articles = 28 points

Advertisement Project Please 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!