1. CONDITIONAL STATEMENTS HONORS GEO 1.6

2. WHAT IS A CONDITIONAL? -A statement that contains “if, then”. -Ex: If you study hard, then you will do well. -Ex: If a triangle contains one right angle, then it is a right triangle. All of the words AFTER “if” are called the hypothesis. All of the words AfTER “then” are called the conckusion. In the above examples, identify the hypothesis and concusion.

3. CONVERSE OF A CONDITIONAL Converse: switch the hypothesis and conclusion. Ex: Conditional - If an angle is obtuse, then it measures more than 90 degrees. Converse – If an angle measures more than 90 degrees, then it is obtuse. ***Sometimes, a conditional statement may be true, but the converse turns out false. Can you think of an example when this happens?

4. COUNTEREXAMPLES If something is false, a “counterexample” is used to prove that it is false. Ex: Conditional - If you live in Hazleton, then you live in Pennsylvania. (TRUE) Converse – If you live in Pennsylvania, then you live in Hazleton. (FALSE) Counterexample – You can live in Pennsylvania, but in Freeland instead. If x squared equals 4, then x equals 2. (FALSE) Provide a counterexample.

5. BICONDITIONAL When a conditional and it’s converse are BOTH TRUE, they can be combined together to form a “biconditional” using the words “if and only if”. Ex: Conditional – If a triangle has no congruent sides, then it is scalene. (TRUE) Converse – If a triangle is scalene, then it has no congruent sides. (TRUE) Because they are both true, we write a “biconditional” from the converse. Biconditional – A triangle is scalene if and only if it has no congruent sides. Create your own example!

6. INVERSE -Negate both the hypothesis and conclusion of the original conditional statement -Ex: -Conditional – If 2x + 5 = 11, then x = 3. -Inverse – If 2x + 5 does not = 11, then x does not = 3. -YOUR TURN

7. CONTRAPOSITIVE Negate both the hypothesis and conclusion of the original conditional statement, and switch them. Ex- Conditional: If you lift weights, then you have muscles. Contrapositive: If you do not have muscles, then you do not lift weights. Your turn

8. DRAWING CONCLUSIONS If you are given a conditional statement and additional information, you can “draw conclusions” (use common sense…don’t make this difficult!!!) Ex: Conditional – If a triangle contains one obtuse angle, then it is an obtuse triangle. Given - ∆ABC has obtuse angle B. Conclusion - Ex: Conditional – If a ray bisects an angle, then it divides the angle into two smaller congruent angles. Given - Ray BD bisects angle ABC. Conclusion -

9. APPLY WHAT YOU LEARNED! 1.Write a conditional and it’s converse that are both true. 2.Write a biconditional. 3.Write the inverse. 4.Write the contrapositive. 5.Write a new conditional that has a false converse. 6.Provide a counterexample.