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Published byRegina Morton Modified over 8 years ago
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Section 2-2: Biconditionals and Definitions
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Conditional: If two angles have the same measure, then the angles are congruent. Converse: If two angles are congruent, then the angles have the same measure. How can we combine both true statements?
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We can combine a true conditional and true converse into a biconditional. We do so by using the phrase “if and only if” to connect the hypothesis and conclusion. Conditional: If two angles have the same measure, then the angles are congruent. Biconditional: Two angles have the same measure if and only if the angles are congruent.
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Remember, it is important for both the conditional AND its converse to be true in order to write a biconditional. Conditional: If a figure is square, then it has four right angles. Can this conditional be written as a biconditional? No, because the converse is false.
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Example: Write the biconditional for the following statement. Conditional: If three points are collinear, then they lie on the same line. Three points are collinear if and only if they lie on the same line.
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Homework: p. 90 #’s 1-17
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