Analyzing and creating conditional statements Whos the Robber

Analyzing and creating conditional statements

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 bailiff • The defense attorney • The district attorney • Courtney Smith • Morgan Button • Kaitlyn Ford • Emma Straight …the remainder of the class is the jury

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. t e l io V Courtney Morgan Kaitlyn Emma Y w o l el B lue B k c la

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!

Unit 2 Section 1: Conditional Statements

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

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

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

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.

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

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. Maybe she didn’t pass the test 8. If a number is divisible by 4 then it is divisible by 6. 16 is divisible by 4 but not 6

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

BICONDITIONAL STATEMENT: When the Conditional and Converse are BOTH TRUE, you can write it as a Biconditional statement, using “if and only if” Example: Two lines are perpendicular if and only if they form right angles. *Definitions can always make biconditional statements.

In-Class Practice Write the conditional and converse of the statement below. If both are true, write the biconditional. An equilateral triangle consists of 3 congruent sides. A triangle is equilateral if and only if it has 3 congruent sides.

Types of Statements Statement CONDITIONAL INVERSE “the nots” CONVERSE “the flips” CONTRAPOSITIVE “the flip nots” Definition If it is a rose, then it is a flower. If it is NOT a rose, then it is NOT a flower. If it is a flower, then it is a rose. If it is NOT a flower, then it is NOT a rose. Symbolic Representation p q ~p ~q q p ~q ~p 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!!