1. 3.5/3.7 Converses, Negations and Contrapositives Warm-up (IN) Learning Objective: to write converses, inverses and contrapositives and use them in logical arguments. A, B, and C are the following statements: True False 1. If A is the hypothesis and C is the conclusion, is the conditional statement True or False? 2. If C is the hypothesis and A is the conclusion, is it True or False? 3. Consider the statement, “If A, then B.” True or False?

2. Notes Converse - The hypothesis and conclusion are switched If a figure is a square, then it has 4 sides. If a figure has 4 sides, then it is a square. Ex 1 – If a quadrilateral is a rhombus, then it has a pair of parallel sides. a. Draw a diagram and state the hyp and concl. B T A O Given: Prove: BOAT is a rhombus BO//TA

3. b. Draw a diagram of the converse and state the hyp and concl. Given: Prove: BOAT is a rhombus BO//TA B T A O CKC p. 138 Conditional - Converse - If P, then Q. If Q, then P. Inverse - If not P, then not Q. Contrapositive - If not Q, then not P.

4. Ex 2 – Rewrite the statement as a conditional, then write the converse, inverse and contrapositive. T or F? A square is a rhombus. Conditional - Converse - Inverse - Contrapositive - If a figure is a square, then it is a rhombus. T If a figure is a rhombus, then it is a square. F If a figure is not a square, then it is not a rhombus. F If a figure is not a rhombus, then it is not a square. T

5. HW – p. 138-139 #4-9,11 p. 151-152 #16-20 Out – Write the converse, inverse and contrapositive of “If I live in Conifer, then I live in Colorado.” T or F? Summary – I have questions about… Quiz Monday – 3.2-3.4