CHAPTER 2 Reasoning and Proof CCCI. 2-1 CONDITIONAL STATEMENTS If you are in this Mrs. Jagoe’s geometry class, then you are not in Mrs. McCreary’s geometry.

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CHAPTER 2 Reasoning and Proof CCCI

2-1 CONDITIONAL STATEMENTS If you are in this Mrs. Jagoe’s geometry class, then you are not in Mrs. McCreary’s geometry class. A conditional statement is an if-then statement. If you are 16, then you can get a driver ’ s license. If you attend South Meck, then you are a Sabre. CCCI

Each conditional statement has two parts: The hypothesis follows the “ if ”. The conclusion follows the “ then ”. If you attend South Meck, then you are a Sabre. Hypothesis Conclusion Note: the hypothesis does not include the word “ if ” ; the conclusion does not include the word “ then ”. CCCI

Underline the hypothesis and circle the conclusion: If I live in Missouri, then I live in the United States. If I eat carrots, then I will have good eyesight. If it is raining, then the ground will get wet. CCCI

Underline the hypothesis and circle the conclusion: If I live in Missouri, then I live in the United States. If I eat carrots, then I will have good eyesight. If it is raining, then the ground will get wet. CCCI

Write the statement as a conditional. Cats have tails. Monday is a weekday. Geometry is awesome! If it is a cat, then it has a tail. If it is a Monday, then it is a weekday. If it is Geometry, then it is awesome! CCCI

Conditionals have a truth value. A conditional can be true or false. If you find a counterexample, the truth value is false. If it is the weekend, then it is Saturday. FALSE Counterexample - Sunday If it is Oct. 31, then it is Halloween. FALSE Counterexample – North Carolina TRUE If you live in the United States, then you live in Missouri. CCCI

The converse of a conditional switches the hypothesis and conclusion. A converse also has a truth value: If you live in Florida, then you live in the United States. If you live in the United States, then you live in Florida. ConditionalConverse T F CCCI

Write the converse. Indicate the truth value of the conditional and its converse. If it is Monday, then it is a weekday. If the month is September, then the month has 30 days. If you are in room 1205 (this room), then you are in this building. If it is Feb. 14, then it is Valentine’s Day. If it is a weekday, then it is Monday. If the month has 30 days, then it is September. If you are in this building, then you are in room If it is Valentine’s Day, then it is Feb. 14. T F T F T F T T CCCI

The Contrapositive negates both the hypothesis and conclusion of the converse. If you live in Florida, then you live in the United States. If you live in the United States, then you live in Florida. If you do not live in the United States, then you do not live in Florida. ConditionalConverseContrapositive CCCI

And the Inverse switches the hypothesis and conclusion of the contrapositive. If you live in Florida, then you live in the United States. If you live in the United States, then you live in Florida. If you do not live in the United States, then you do not live in Florida. If you do not live in Florida, then you do not live in the United States. ConditionalConverseContrapositiveInverse CCCI

If – then statement sort CONDITIONAL CONVERSE CONTRAPOSITIVE INVERSE You have 4 sets of cards. Group by topic. The one in bold is the conditional. Then arrange as shown with the converse, contrapositive, and inverse statements below their corresponding conditional. If a figure is a rectangle, then it has four sides If it is Monday, then it is a weekday. If it is March, then the month has 31 days. If your teacher's name is Mrs. Jagoe, then you are in Geometry class. CCCI

If – then statement sort CONDITIONAL CONVERSE CONTRAPOSITIVE INVERSE You have 4 sets of cards. Group by topic. The one in bold is the conditional. Then arrange as shown with the converse, contrapositive, and inverse statements below their corresponding conditional. If a figure is a rectangle, then it has four sides If a figure has four sides, then it is a rectangle. If a figure does not have four sides, then it is not a rectangle. If a figure is not a rectangle, then it does not have four sides. If it is Monday, then it is a weekday. If it is a weekday, then it is a Monday. If it is not a weekday, then it is not a Monday. If it is not a Monday, then it is not a weekday. CCCI

If – then statement sort CONDITIONAL CONVERSE CONTRAPOSITIVE INVERSE You have 4 sets of cards. Group by topic. The one in bold is the conditional. Then arrange as shown with the converse, contrapositive, and inverse statements below their corresponding conditional. If it is March, then the month has 31 days. If the month has 31 days, then it is March. If the month does not have 31 days, then it is not March. If it is not March, then the month does not have 31 days. If your teacher's name is Mrs. Jagoe, then you are in Geometry class. If you are in Geometry class, then your teacher's name is Mrs. Jagoe. If you are not in Geometry class, then your teacher's name is not Mrs. Jagoe. If your teacher's name is not Mrs. Jagoe, then you are not in Geometry class. CCCI

Glue in your notebook. When finished… write in your journal So what… now what??? CCCI