2.2.1 Analyze Conditional Statements and Proof Chapter 2: Reasoning and Proof.

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Presentation transcript:

2.2.1 Analyze Conditional Statements and Proof Chapter 2: Reasoning and Proof

Definitions Conditional Statements – Logical statement that has 2 parts Hypothesis and Conclusion Usually written as If – Then The If part is the hypothesis The Then part is conclusion If x = 2 then x 2 = 4 Hypothesis Conclusion Identify the Hypothesis and conclusion then Convert this sentence into an If-Then Statement: Two angles are supplementary if they are a Linear Pair

Related Conditionals The converse of a statement is when the hypothesis and the conclusion are switched: (sometimes true) The inverse of a statement is when the hypothesis and the conclusion are negated (sometimes true) Add the word not to both to negate The Contrapositive of a statement is when the combination of inverse and Converse are applied to a statement: (true if original is true) If I am human then I am a manIf I am a man then I am human If I am man then I am a humanIf I am not a man then I am not a human If I am man then I am a human If I am not a human then I am not a man

Write the statement as a conditional, rewrite as a converse and determine truth values Statement:  A is obtuse because m  A = 99 ⁰ Converse: Statement: The measures of two supplemental angles add to 180⁰ Converse: Truth Value:

Write the statement as a conditional, rewrite as a converse and determine truth values Statement: All Rectangles are Squares Converse: Statement: Isosceles triangles have two congruent sides Converse: Truth Value:

Homework pp. 82 – 85 1, 4, 5, 9, 10, 14, 15, 27, 29, 30