Inverses and Contrapositives

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# Inverses and Contrapositives - PowerPoint PPT Presentation

Inverses and Contrapositives. 9.3.2.2 Accurately interpret and use words and phrases in geometric proofs such as &quot;if…then,&quot; &quot;if and only if,&quot; &quot;all,&quot; and &quot;not.&quot; Recognize the logical relationships between an &quot;if…then&quot; statement and its inverse, converse and contrapositive. .

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### Inverses and Contrapositives

9.3.2.2 Accurately interpret and use words and phrases in geometric proofs such as "if…then," "if and only if," "all," and "not." Recognize the logical relationships between an "if…then" statement and its inverse, converse and contrapositive.

Lesson Objective: Iwbat convert a conditional statement into its inverse and contrapositive.

• Write the following as a conditional and then write the converse.
• Two angles whose sum is 90 are complementary.
Guiding Question: How do I negate conditional statements?

The inverse and contrapositive of statement say the opposite of a statement.

• Inverse – negate the conditional (if –p then –q)
• Contrapositive – switch the conclusion and hypothesis of the inverse.
• Conditional Statement

If 2 angles are vertical, then they are congruent.

• What is the hypothesis?
• What is the conclusion?
• What is the inverse?
• What is the contrapositive?
Guiding Question: How do I negate conditional statements?

“Today is Wednesday”

• Write the conditional
• Write the converse
• Write the inverse
• Write the contrapositive
Guiding Question: How do I negate conditional statements

“The Lion is the King of the Jungle”

• Write the conditional statement
• Write the converse
• Write the inverse
• Write the contrapositive
Guiding Question: How do I negate conditional statements?