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(5-4) I NVERSES AND CONTRAPOSITIVES Learning Targets: To write the negation of a statement. To write the inverse and the contrapositive of a conditional statement. Purpose: Be able to recognize these special types of statements in a proof.

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Example: Two angles are congruent. Two angles are not congruent. (5.4) Negation The negation of a statement has the opposite meaning of the original statement.

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Example: Conditional: If a figure is a square, then it is a rectangle. Inverse: If it is not a square, then it is not a rectangle. (5.4) Inverse The inverse of a conditional statement negates both the hypothesis and the conclusion.

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Example: Conditional: If a figure is a square, then it is a rectangle. Contrapositive: If it is not a rectangle, then it is not a square. (5.4) Contrapositive The contrapositive of a conditional statement switches the the hypothesis and the conclusion and negates both.

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Example: Write the (a) the inverse and (b) contrapositive of Maya Angelou’s statement. (5.4) Contrapositive The contrapositive of a conditional statement switches the the hypothesis and the conclusion and negates both. “If you don’t stand for something, then you’ll fall for anything.”

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Example: Identify the two statements that contradict each other. (When they both cannot be true at the same time. ) I. ABC is acute II. ABC is scalene III. ABC is equiangular (5.4) Identifying Contradictions A triangle can be acute and scalene. So I and II do not contradict each other. An equiangular triangle is an acute triangle. So I and III do not contradict each other. An equiangular triangle must be equilateral, so it cannot be scalene. II and III contradict each other.

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HOMEWORK (5.4) Pgs. 283-284; 2-6 evens, 7-9 all and 16-19 all

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