Get one of these

1. Get one of these Think about *linear pairs *degrees in a triangle *degrees in a quadrilateral

2. Warm up Make a new notebook then do the problems below. • 2x + 3 = 4 + 5x • X = -1/3 • 43 + 22 + 67 = 5x – 2 • X = 134/5 • √4 • +2, -2 • √9 • +3, -3 • √36 • +6, -6

3. 2.2 Intro to Logic Conditional Statements If-then form: If a car is a Corvette, then it is a Chevrolet. Notation: If p then q or p q Picking it apart: Ifa car is a Corvette,thenit is a Chevrolet. hypothesis conclusion (Notice “if” and “then” are not part of the hypothesis and conclusion.)

4. Euler diagrams(pronounced “Oiler”) • Often called Venn diagrams. Be sure you know both names. • Our example: If a car is a Corvette, then it is a Chevrolet. • Since all Corvettes are Chevrolets, and Corvettes are just a piece of the Chevrolet line, here is what the Euler looks like: • (it would be safe to say that the hypothesis goes ‘inside’ while the conclusion goes ‘outside’.) Corvettes

5. What about Susan? • Consider this: • Susan’s car is a Corvette. • Where does it belong in the diagram? (With Chevrolets or with Corvettes?) • Corvettes • Susan’s car • The complete process of drawing a conclusion is called a logical argument. • This 3 part argument is called a syllogism

6. Our SYLLOGISM about Susan(3 parts) 1. If a car is a Corvette, then it is a Chevrolet. 2. Susan’s car is a Corvette. 3. Therefore, Susan’s car is a Chevrolet.

7. Try this: • (Remember that an equilateral triangle is a triangle with 3 congruent sides.) • (Remember that an isosceles triangle is a triangle with at least 2 congruent sides.) Isoceles Triangles Equilateral Triangles ∆ ABC Draw an Euler diagram that conveys the following information: If a triangle is equilateral, then the triangle is isosceles. ∆ ABC is equilateral. What conclusion can you draw about ∆ ABC ? ∆ ABC IS ISOSCELES.

8. CONVERSE A converse statement switches the hypothesis and conclusion of the conditional statement. (The ‘if’ and ‘then’ stay put) Conditional: If a car is a Corvette, then it is a Chevrolet. Converse: If a car is a Chevrolet, then it is a Corvette.

9. Logical Chains Consider this: If cats freak, then mice frisk. If sirens shriek, then dogs howl. If dogs howl, then cats freak. We need to put these statements in a logical order…. So…. The easiest way is to find a conclusion that matches a hypothesis and make a zig-zag pattern: If sirens shriek, then dogs howl. If dogs howl, then cats freak. If cats freak, then mice frisk. CONCLUSION: If sirens shriek, then mice frisk.

10. The Logical Chain is also called: • Transitive Property. If A then B, And if B then C Conclusion: If A then C.

11. Quick Review • What is another name for an if-then statement? • What is the hypothesis part of an if-then statement? • What is the conclusion part of an if-then statement? • How do we make converse statement? • What is an Euler diagram? • Explain the Transitive property? • How would you write this as a conditional statement: All people who live in Ohio live in the United States. • How would you write the previous statement as a converse statement?

12. Assignment • Pg 95, 9-33 all, ≠ 29