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Section 2-2 Biconditional Statements. Biconditional statement a statement that contains the phrase “if and only if”. Equivalent to a conditional statement.

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Presentation on theme: "Section 2-2 Biconditional Statements. Biconditional statement a statement that contains the phrase “if and only if”. Equivalent to a conditional statement."— Presentation transcript:

1 Section 2-2 Biconditional Statements

2 Biconditional statement a statement that contains the phrase “if and only if”. Equivalent to a conditional statement and its converse.

3 We can use iff to stand for “If and only if”

4 In order for a biconditional statement to be TRUE, both the conditional statement and its converse must be true.

5 Example #1: Two lines intersect if and only if their intersection is exactly one point. Write this biconditional statement as a conditional statement.

6 If two lines intersect, then their intersection is exactly one point. True Conditional Statement:

7 If their intersection is exactly one point, then two lines intersect. Now write the converse. True

8 Example #2 Three lines are coplanar if and only if they lie in the same plane. Write this biconditional statement as a conditional statement.

9 If three lines are coplanar, then they lie in the same plane. True Conditional Statement:

10 If three lines lie in the same plane, then they are coplanar. Now write the converse. True

11 If an angle is acute then it has a measure between 0° and 90°. Write the conditional as a biconditional statement.

12 Write the converse If an angle has a measure between 0° and 90°, then it is acute. True

13 If it is true, then a biconditional can be written If it is false, then a biconditional CAN NOT be written. Identify whether the converse is true or false

14 Bicondtional: An angle is acute if and only if it has a measure between 0° and 90°.

15 If an animal is a leopard, then it has spots. Write the conditional as a biconditional statement. Write the converse. If an animal has spots, then is a leopard. False

16 Therefore a biconditional for this statement does not exist!

17 More Examples: Try It! Write each conditional as a biconditional statement, if possible. Be sure to give a counterexample if the converse is false!

18 1.If is perpendicular to, then their intersection forms a right angle. Converse: If, and intersect at a right angle, then they are perpendicular to each other. True

19 is perpendicular to iff their intersection forms a right angle. Biconditional:

20 2. If x 2 < 49, then x < 7 If x < 7, then x 2 < 49. Counterexample: let then Therefore, a biconditional can not be written! Converse:

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