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**What is the length of AB What is length of CD**

Warm Up March 12, 2014 B D, E, and F are midpoints. 10 8 D E 4 What is the length of AB What is length of CD G 8 A C F

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EOCT Week 9 #3

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**Conditional Statements**

Also known as logic statements. Types: Conditional, Inverse, Converse, & Contrapositive

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**a. Conditional Statements**

Called if-then statements Have 2 parts Hypothesis- The part after if. Conclusion- The part after then. * Do not include if and then in the hypothesis and conclusion.

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**Hypothesis and Conclusion**

Example: If you are not satisfied for any reason, then return everything within 14 days for a full refund.

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**p: A figure is a rectangle. q: The diagonals are congruent.**

A compound statement joined with an if…then. CONDITIONAL p: A figure is a rectangle. q: The diagonals are congruent. If p then q: If a figure is a rectangle, then the diagonals are congruent.

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**Examples: Identify the Hypothesis and the conclusion.**

1. If it is Saturday, then Beckham plays soccer. Hypothesis- Conclusion- 2. If points are collinear, then they lie on the same line. it is Saturday Beckham plays soccer points are collinear they lie on the same line

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Negation A statement can be altered by negation by writing the negative of the statement Symbol: ~

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b. Inverse When you negate the hypothesis and conclusion of a conditional statement, you form the inverse.

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Inverse The inverse of a conditional statement is formed by negating both the hypothesis and the conclusion in the conditional (Add “NOT”) Conditional- If a figure is a triangle, then it has three angles. Inverse- If a figure is not a triangle, then it does not have three angles.

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**p: A figure is a rectangle. q: The diagonals are congruent.**

INVERSE Negating a conditional. p: A figure is a rectangle. q: The diagonals are congruent. If ~p then ~q: If the figure is not a rectangle, then the diagonals are not congruent.

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c. Converse The converse of a conditional statement swaps the hypothesis and the conclusion. Conditional- If a figure is a triangle, then it has three angles. Converse- If a figure has three angles, then it is a triangle.

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**p: A figure is a rectangle. q: The diagonals are congruent.**

Exchange the p and q of a conditional statement. CONVERSE p: A figure is a rectangle. q: The diagonals are congruent. If q then p: If the diagonals are congruent, then the figure is a rectangle.

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*** Converses are not always true.**

Conditional- If a figure is a square, then it has four sides. Converse- If a figure has four sides, then it is a square. * Not all four sided figures are squares. Rectangles also have four sides.

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**Counterexample Giving at least 1 example that disproves the statement.**

Example: All prime numbers are odd.

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d. Contrapositive When you negate the hypothesis and conclusion of the converse of a conditional statement, you form the contrapositive.

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**(SWITCH the order and NEGATE)**

Contrapositive The contrapositive of a conditional statement is formed by switching and negating both the hypothesis and the conclusion. (SWITCH the order and NEGATE) Conditional- If a figure is a triangle, then it has three angles. Contrapositive- If it does not have three angles, then a figure is not a triangle.

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**p: A figure is a rectangle. q: The diagonals are congruent.**

Contrapositive Negating the converse. p: A figure is a rectangle. q: The diagonals are congruent. If ~q then ~p: If the diagonals are not congruent, then the figure is not a rectangle.

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Recap Conditional: p → q Inverse: ~p → ~ q Converse: q → p Contrapositive: ~ q → ~ p

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Truth Value Decide whether the statement is true or false. If false, give a counterexample as to why it’s false. STMT: If you are a basketball player, then you are an athlete. Converse: Inverse: Contrapositive: False, not all athletes play basketball. Could play baseball, golf, tennis, swim, etc. False, even if you don’t play basketball, you can still be an athlete. Again, could play baseball, golf, tennis, swim, etc. True

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**Give me some statements!!**

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