Biconditional 5 x 8 37 if and only if x 9 Biconditional Two angles have the

# Biconditional 5 x 8 37 if and only if x 9

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Biconditional: 5 x – 8 = 37 if and only if x = 9. Biconditional: Two angles have the same measure if and only if they are congruent.
Holt McDougal Geometry 2-4 Biconditional Statements and Definitions Check It Out! Example 2a If the date is July 4th, then it is Independence Day. For the conditional, write the converse and a biconditional statement. Converse: If it is Independence Day, then the date is July 4th. Biconditional: It is July 4th if and only if it is Independence Day.
Holt McDougal Geometry 2-4 Biconditional Statements and Definitions Check It Out! Example 2b For the conditional, write the converse and a biconditional statement. If points lie on the same line, then they are collinear. Converse: If points are collinear, then they lie on the same line. Biconditional: Points lie on the same line if and only if they are collinear.
Holt McDougal Geometry 2-4 Biconditional Statements and Definitions For a biconditional statement to be true, both the conditional statement and its converse must be true. If either the conditional or the converse is false, then the biconditional statement is false.
Holt McDougal Geometry 2-4 Biconditional Statements and Definitions Determine if the biconditional is true. If false, give a counterexample. Example 3A: Analyzing the Truth Value of a Biconditional Statement A rectangle has side lengths of 12 cm and 25 cm if and only if its area is 300 cm 2 .
Holt McDougal Geometry 2-4 Biconditional Statements and Definitions Example 3A: Analyzing the Truth Value of a Biconditional Statement Conditional: If a rectangle has side lengths of 12 cm and 25 cm, then its area is 300 cm 2 . Converse: If a rectangle’s area is 300 cm 2 , then it has side lengths of 12 cm and 25 cm. The conditional is true. The converse is false. If a rectangle’s area is 300 cm 2 , it could have side lengths of 10 cm and 30 cm. Because the converse is false, the biconditional is false.
Holt McDougal Geometry 2-4 Biconditional Statements and Definitions Determine if the biconditional is true. If false, give a counterexample. Example 3B: Analyzing the Truth Value of a Biconditional Statement A natural number n is odd n 2 is odd. Conditional: If a natural number n is odd, then n 2 is odd. The conditional is true. Converse: If the square n 2 of a natural number is odd, then n is odd. The converse is true. Since the conditional and its converse are true, the biconditional is true.
Holt McDougal Geometry 2-4 Biconditional Statements and Definitions Check It Out! Example 3a An angle is a right angle iff its measure is 90°. Determine if the biconditional is true. If false, give a counterexample.

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• Winter '17
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