1. Section 2-5: Deductive Reasoning Goal: Be able to use the Law of Detachment and the Law of Syllogism. Inductive Reasoning uses _________ to make conclusions. Deductive Reasoning uses ___________ to make conclusions. rules ____________________ examples hypothesis conclusion true Law of Detachment If the ____________ of a true if-then statement is _______, then the ___________ is also ______. true

2. Use the Law of Detachment to draw a conclusion. 1.) If a vehicle is a car, then it has four wheels. Conclusion: _____________________________A Jeep has four wheels. true A Jeep is a car. true 2.) If two lines are parallel, then they do not intersect. Line m is parallel to line n. Conclusion: _____________________________Line m and line n do not intersect. true

3. 3.) Which argument is correct? Explain your reasoning. Argument 1: If two angles form a linear pair, then they are supplementary. and form a linear pair. So, and are supplementary. Argument 2: If two angles form a linear pair, then they are supplementary. and are supplementary. So, and form a linear pair. In Argument 1, the hypothesis is true, which implies the conclusion is true. Argument 2 is false because two nonadjacent angles could be supplementary, for example 30° and 150°, but not form a linear pair.

4. 4.) Which argument is correct? Explain your reasoning. Argument 1: If two angles measure 70° and 110°, then the angles are supplementary. and are supplementary. So and Argument 2: If two angles measure 70° and 110°, then the angles are supplementary. The and. So, and are supplementary. In Argument 2, the hypothesis is true, which implies the conclusion is true. Argument 1 is false because angle 1 could be 60° and angle 2 120°. They are supplementary, but their measures are not 70° and 110°.

5. Law of Syllogism_______________ 5.) If a quadrilateral is a square, then it contains four right angles. Use the Law of Syllogism to draw a conclusion. If a quadrilateral contains four right angles, then it is a rectangle. Conclusion: __________________________________ _____________________________________________ pq qr If a quadrilateral is a square,If p, then r. then it is a rectangle. If statement p, then statement q. If statement q, then statement r. If statement p, then statement r. If these statements are true, then this statement is true

6. 6.) If people live in Vernon Hills, then they live in Illinois. If people live in Illinois, then they live in the United States. Conclusion: __________________________________ _____________________________________________ If people live in Vernon Hills,If p, then r. then they live in the United States. p q r q As a group, write your own conclusions based on the Law of Detachment and the Law of Syllogism. Each group member will take a turn in creating a sentence that makes sense in reaching a conclusion.

7. Write your own example to illustrate the correct use of the Law of Detachment. Write your own example to illustrate the correct use of the Law of Syllogism. 1.) __________________________________________________________ ____________________________________________________________ 2.) __________________________________________________________ 3.) __________________________________________________________ ____________________________________________________________ 1.) __________________________________________________________ ____________________________________________________________ 2.) __________________________________________________________ ____________________________________________________________ 3.) __________________________________________________________ ____________________________________________________________