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**Geometry 2.2 Big Idea: Analyze Conditional Statements**

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Conditional Statement: A logical statement with 2 parts, a hypothesis and a conclusion. IF (hypothesis) THEN (conclusion)

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**Statements of fact can be rewritten in IF-THEN Form. Ex**

Statements of fact can be rewritten in IF-THEN Form. Ex.1) Ants are insects. If it is an ant, then it is an insect.

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**Ex. 2) When x = 6, x2 = 36. If x = 6, then x2 = 36. **

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**Just like conjectures, a conditional statement can be True or False**

Just like conjectures, a conditional statement can be True or False. If True , you would have to prove all examples are True. If False, you need only provide one counterexample.

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**Converse: Switch the hypothesis and conclusion**

Converse: Switch the hypothesis and conclusion. Converses can be True or False, as well.

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Converse: Ex. If it is an insect, then it is an ant (True/False ?) (Counterexample of Converse: A mosquito is an insect but it’s not an ant.)

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**Conditional Statement: If 2 rays are opposite rays, then they have a common endpoint.**

(True/False ?) Converse: If 2 rays have a common endpoint, then they are opposite rays. (True/False ?)

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Conditional statements and their converses can both be true, both be false or have only one be true. No assumptions can be made.

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Inverse: Negate (say it’s not true) both the hypothesis and the conclusion. If it is not an ant, then it is not an insect. (True/False ?)

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Contrapositive: Negate both the hypothesis and conclusion in the converse of the conditional statement.

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**Ex. If it not an insect, then it is not an ant. (True/False ?)**

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Summary C.S.: If it is an ant, then it is an insect. (T) Conv.: If it is an insect, then it is an ant. (F) Inv.: If it is not an ant, then it is not an insect. (F) Contra.: If it is not an insect, then it is not an ant. (T)

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A conditional statement and its contrapositive (the negation of the converse) are always either both False or both True. This is also true for the converse and the inverse.

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**Equivalent Statements:**

If two statements are both true or both false. Ex.1) C.S. and its contrapositive Ex.2) converse and inverse

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Biconditional Statement: Contains phrase “If and only If” (can be written only when the C.S. and its converse are true) Any good definition can be written as a biconditional statement.

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C.S.: If 2 rays are opposite rays, then they share a common endpoint and lie on the same line. Biconditional Statement: Two rays are opposite if and only if they share a common endpoint and lie on the same line.

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