3.5/3.7 Converses, Negations and Contrapositives Learning Objective: to write converses, inverses and contrapositives and use them in logical arguments. Warm-up (IN) A, B, and C.

Learning Objective: to write converses, inverses and contrapositives and use them in logical arguments.

Warm-up (IN)

A, B, and C are the following statements: A :  1 and  2 are vertical angles.

B C :  1 and  2 are adjacent angles.

:  1 and  2 are congruent.

1. If A is the hypothesis and C is the conclusion, is the conditional statement True or False?

True 2. If C is the hypothesis and A is the conclusion, is it True or False?

False 3. Consider the statement, “If A, then B.” True or False?

False

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 O Given: BOAT is a rhombus Prove: BO//TA T A

b. Draw a diagram of the converse and state the hyp and concl.

B O Given: BO//TA Prove: BOAT is a rhombus T A

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 .

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 If a figure is a square, then it is a rhombus.

If a figure is a rhombus, then it is a square.

F T Inverse If a figure is not a square, then it is not a rhombus.

F Contrapositive If a figure is not a rhombus, then it is not a square.

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…

HW – p. 138-139 #4-9,11 p. 151-152 #16-20