Learning Targets I can recognize conditional statements and

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Learning Targets I can recognize conditional statements and their parts. I can write the

Learning Targets I can recognize conditional statements and their parts. I can write the converse of conditional statements. 11/24/2020 Geometry 4

Conditional Statement A conditional statement has two parts, a hypothesis and a conclusion. When

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 11/24/2020 Geometry 5

Example 1: State the hypothesis and conclusion. If you are 13 years old, then

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 11/24/2020 Geometry 6

Example 1: Rewrite in the if-then form All mammals breathe oxygen If an animal

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. 11/24/2020 Geometry 7

Negation The negative of the statement Example: Write the negative of the statement A

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 11/24/2020 Geometry 8

Converse, Inverse and Contrapositive Converse The converse of a conditional is formed by switching

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 11/24/2020 Geometry ~q → ~p. 9

Example Write the (a) inverse, (b) converse, and (c) contrapositive of the statement. If

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. 11/24/2020 Geometry 10

Equivalent Statements When 2 statements are both true or both false A conditional statement

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. 11/24/2020 Geometry 11

11/24/2020 Conditional Statement Converse Inverse Contrapositive Geometry 12

11/24/2020 Conditional Statement Converse Inverse Contrapositive Geometry 12

Nested conditional statements Nested conditional statements A conditionalNested conditional statements Nested conditional statements A conditional
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CONDITIONAL STATEMENTS Section 2 3 Conditional Statements ConditionalCONDITIONAL STATEMENTS Section 2 3 Conditional Statements Conditional
Conditional Statements and Conditional Statements Biconditional Statements WarmConditional Statements and Conditional Statements Biconditional Statements Warm
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CONDITIONAL CLAUSES Conditional Sentences First Conditional Real ConditionalCONDITIONAL CLAUSES Conditional Sentences First Conditional Real Conditional
Conditional Statements Goals Recognize a conditional statement WriteConditional Statements Goals Recognize a conditional statement Write
Conditional Statements 1 Conditional Statement Definition A conditionalConditional Statements 1 Conditional Statement Definition A conditional