1. Lesson 2-5 1 Conditional Statements

2. Lesson 2-5 2 Conditional Statement Definition:A conditional statement is a statement that can be written in if-then form. “If _____________, then ______________.” Example:If your feet smell and your nose runs, then you're built upside down. Continued……

3. Lesson 2-5 3 Conditional Statement - continued Conditional Statements have two parts: The hypothesis is the part of a conditional statement that follows “if” (when written in if-then form.) The conclusion is the part of an if-then statement that follows “then” (when written in if-then form.) The hypothesis is the given information, or the condition. The conclusion is the result of the given information.

4. Lesson 2-5 4 Conditional statements can be written in “if-then” form to emphasize which part is the hypothesis and which is the conclusion. Writing Conditional Statements Hint: Turn the subject into the hypothesis. Example 1:Vertical angles are congruent.can be written as... If two angles are vertical, then they are congruent. Conditional Statement: Example 2:Seals swim. can be written as... Conditional Statement: If an animal is a seal, then it swims.

5. Lesson 2-5 5 If …Then vs. Implies Two angles are vertical implies they are congruent. Another way of writing an if-then statement is using the word implies. If two angles are vertical, then they are congruent.

6. Lesson 2-5 6 Conditional Statements can be true or false: A conditional statement is false only when the hypothesis is true, but the conclusion is false. A counterexample is an example used to show that a statement is not always true and therefore false. If you live in N.C., then you live in Raleigh.Statement: Counterexample:I live in NC, BUT I live in Kernersville. Is there a counterexample? Therefore (  ) the statement is false. Yes !!!

7. Lesson 2-5 7 Forms of Conditional Statements Converse: Switch the hypothesis and conclusion If two angles are vertical, then they are congruent. If two angles are congruent, then they are vertical. Continued…..

8. Lesson 2-5 8 Forms of Conditional Statements Inverse: State the opposite of both the hypothesis and conclusion. If two angles are vertical, then they are congruent. If two angles are not vertical, then they are not congruent.

9. Lesson 2-5 9 Forms of Conditional Statements Contrapositive: Switch the hypothesis and conclusion and state their opposites. If two angles are vertical, then they are congruent. If two angles are not congruent, then they are not vertical.

10. Lesson 2-5 10 Forms of Conditional Statements Contrapositives are logically equivalent to the original conditional statement.

11. Lesson 2-5 11 Biconditional When a conditional statement and its converse are both true, the two statements may be combined. Use the phrase if and only if (sometimes abbreviated: iff) Statement: If an angle is right then it has a measure of 90 . Converse: If an angle measures 90 , then it is a right angle. Biconditional: An angle is right if and only if it measures 90 .

12. Lesson 2-5 12 Law of Detachment Given: a true conditional statement and the hypothesis occurs Conclusion: the conclusion will also occur

13. Lesson 2-5 13 Law of Detachment - Example Given: If three points are collinear, then the points are all on one line. E, F, and G are collinear. Conclusion: E, F, and G are all on one line. Example 1: Given: If I find $20 in the street, then I’ll take you to the movies. On October 10 I found $20 in the street. Conclusion: I will take you to the movies. Example 2:

14. Lesson 2-5 14 Law of Syllogism Given: Two true conditional statements and the conclusion of the first is the hypothesis of the second. Conclusion: If the hypothesis of the first occurs, then the conclusion of the second will also occur.

15. Lesson 2-5 15 Law of Syllogism - Example If it rains today, then we will not see our friends. Example: If it rains today, then we will not have a picnic. If we do not have a picnic, then we will not see our friends. Conclusion: Given: