Analyzing and creating conditional statements

1. Who's the Robber? Analyzing and creating conditional statements

2. Who’s the Robber? We are going to create a courtroom scenario in which the jury is to determine who robbed a bank. We need someone to play the parts of: …the remainder of the class is the jury • The bailiff • The defense attorney • The district attorney • Courtney Smith • Morgan Button • Kaitlyn Ford • Emma Straight

3. Who’s the Robber? Members of the jury: You’re job is to determine whether Courtney Smith robbed the bank. In order to do this, listen to the testimony. Draw the following chart on your paper to help you determine if Courtney is the robber. Blue Violet Black Yellow Courtney Morgan Kaitlyn Emma

4. Who’s the Robber? Conclusion Members of the Jury: Explain the reasoning used to determine which person drove each color car. The statements that you used to draw your conclusions are called CONDITIONAL STATEMENTS, and this is what we are talking about today!

5. Unit 2 Section 2:Conditional Statements

6. Conditional Statements CONDITIONAL STATEMENT: Hypothesis: The part after ______ Conclusion: The part after _______ An IF-THEN statement with two parts, an hypothesis and a conclusion. if then

7. Examples of Conditional Statements CONDITIONAL: ALL panthers are cats If-Then Form: CONDITIONAL: The sum of 2 odd integers is even. If-then Form: If an animal is a panther, then it is a cat. If two integers are odd, then their sum is even.

8. In-Class Practice Write each statement as an If-Then Statement. 1. Congruent segments are segments that have equal lengths. 2. An equilateral triangle consists of three congruent angles and three equal sides. If segments are congruent, then the segments have equal lengths. If a polygon is an equilateral triangle, then it has 3 congruent angles and 3 equal sides.

9. In-Class Practice Underline the hypothesis and circle the conclusion of each conditional statement. (Think of how you’d write it in IF-THEN form) 3. VW = XY implies VW  XY 4. K is the midpoint of JL if JK = KL 5. Mr. Scroggins sings when all his students get an A on the test. 6. People who live in Texas, live in the US..

10. Counterexamples COUNTEREXAMPLE: A specific case for which the conjecture is false.

11. In-Class Practice Provide a counterexample to disprove the statement. 7. If Rachel is 16 years old, then she has obtained her driver’s license. 8. If a number is divisible by 4 then it is divisible by 6. Maybe she didn’t pass the test 16 is divisible by 4 but not 6

12. OTHER CONDITIONALS Switch the hypothesis and conclusion. CONVERSE: INVERSE: CONTRAPOSITIVE: Negate the hypothesis and conclusion. Write the converse and then negate the hypothesis and conclusion.

13. Types of Statements If p, then q p  q If it is a rose, then it is a flower. If NOT p, then NOT q ~ p  ~q If it is NOT a rose, then it is NOT a flower. “the nots” If q, then p q  p “the flips” If it is a flower, then it is a rose. If NOT q, then NOT p ~q  ~p “the flip nots” If it is NOT a flower, then it is NOT a rose. The Conditional and Contrapositive are related – if one is true, they are both true. The Inverse and Converse are related – if one is true, they are both true or if one is false, they are both false!!

14. Summary Conditional NOTS INVERSE FLIPS CONVERSE FLIP NOTS CONTRAPOSITIVE

15. Elaborate! • Get in groups of 2 – 4 to complete the 2.2 Logical Reasoning (“if-then” statements) Worksheet