2. Concept

3. The word if is not part of the hypothesis. The word then is not part of the conclusion.

4. Example 1 Identify the Hypothesis and Conclusion Identify the hypothesis and conclusion of the following statement. Answer:Hypothesis: A polygon has 6 sides. Conclusion: It is a hexagon. If a polygon has 6 sides, then it is a hexagon. hypothesis conclusion

5. A.A B.B C.C D.D Example 2 A.If an octagon has 8 sides, then it is a polygon. B.If a polygon has 8 sides, then it is an octagon. C.If a polygon is an octagon, then it has 8 sides. D.Two of the above answers are correct. A. Which of the following is the correct if-then form of the given statement? A polygon with 8 sides is an octagon.

6. A.A B.B C.C D.D Example 2 A.If an angle is acute, then it measures less than 90°. B.If an angle is not obtuse, then it is acute. C.If an angle measures 45°, then it is an acute angle. D.If an angle is acute, then it measures 45°. B. Which of the following is the correct if-then form of the given statement? An angle that measures 45° is an acute angle.

7. Concept

9. What is a biconditional? In logic, a biconditional is a compound statement formed by combining two conditionals under "and." Biconditionals are true when both statements (facts) have the exact same truth value.

10. Definitions are very important in mathematics so that we can all agree upon an acceptable usage of a term. A good geometric definition is one in which the definition can be written as a conditional statement in which the statement and its converse are both true. Huh?!?!

11. Look at this definition for perpendicular lines.

12. Since both the conditional and the converse are true, this is a good definition. Good definitions can be written as something we call a biconditional. Biconditionals are two statements joined by if and only if. If and only if guarantees a form of uniqueness.

13. EXAMPLE 4 Write a biconditional Write the definition of perpendicular lines as a biconditional. SOLUTION Definition: If two lines intersect to form a right angle, then they are perpendicular. Converse: If two lines are perpendicular, then they intersect to form a right angle. Biconditional: Two lines are perpendicular if and only if they intersect to form a right angle.

14. GUIDED PRACTICE for Example 4 Rewrite the definition of right angle as a biconditional statement. Biconditional: An angle is a right angle if and only if the measure of the angle is 90°