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Learning Targets I can recognize conditional statements and their parts. I can write the converse of conditional statements. 6/1/2016Geometry4.

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Presentation on theme: "Learning Targets I can recognize conditional statements and their parts. I can write the converse of conditional statements. 6/1/2016Geometry4."— Presentation transcript:

1 Learning Targets I can recognize conditional statements and their parts. I can write the converse of conditional statements. 6/1/2016Geometry4

2 Conditional Statement A conditional statement has two parts, a hypothesis and a conclusion. When conditional statements are written in if-then form, the part after the “if” is the hypothesis, and the part after the “then” is the conclusion. p → q 6/1/2016Geometry5

3 Example 1: State the hypothesis and conclusion. If you are 13 years old, then you are a teenager. Hypothesis: You are 13 years old Conclusion: You are a teenager 6/1/2016Geometry6

4 Example 1: Rewrite in the if-then form All mammals breathe oxygen If an animal is a mammal, then it breathes oxygen. A number divisible by 9 is also divisible by 3 If a number s divisible by 9, then it is divisible by 3. 6/1/2016Geometry7

5 Negation The negative of the statement Example: Write the negative of the statement  A is acute  A is not acute ~p represents “not p” or the negation of p 6/1/2016Geometry8

6 Converse, Inverse and Contrapositive Converse The converse of a conditional is formed by switching the hypothesis and the conclusion. The converse of p → q is q → p Inverse Negate the hypothesis and the conclusion The inverse of p → q, is ~p → ~q Contrapositive Negate the hypothesis and the conclusion of the converse The contrapositive of p → q, is ~q → ~p. 6/1/2016Geometry9

7 Example Write the (a) inverse, (b) converse, and (c) contrapositive of the statement. If two angles are vertical, then the angles are congruent. (a) Inverse: If 2 angles are not vertical, then they are not congruent. (b) Converse: If 2 angles are congruent, then they are vertical. (c) Contrapositive: If 2 angles are not congruent, then they are not vertical. 6/1/2016Geometry10

8 Equivalent Statements When 2 statements are both true or both false A conditional statement is equivalent to its contrapositive. The inverse and the converse of any conditional are equivalent. 6/1/2016Geometry11

9 6/1/2016Geometry12 Conditional StatementConverse InverseContrapositive

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