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Understanding Inverses and Contrapositives in Geometric Proofs

This lesson focuses on the concepts of inverses and contrapositives in geometry. Students will learn to accurately interpret and use phrases such as "if...then" and "if and only if" in geometric proofs. The objective is to convert conditional statements into their inverses and contrapositives. Through guided questions, students will explore how to negate conditional statements and recognize logical relationships. Practice exercises include writing conditional statements, converses, inverses, and contrapositives for various examples.

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Understanding Inverses and Contrapositives in Geometric Proofs

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  1. 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.

  2. 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?

  3. 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?

  4. “Today is Wednesday” • Write the conditional • Write the converse • Write the inverse • Write the contrapositive Guiding Question: How do I negate conditional statements

  5. “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?

  6. Assignment: Inverse and Contrapositive WS Guiding Question: How do I negate conditional statements?

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