This document discusses conditional statements and their components. It defines a conditional statement as having a hypothesis and conclusion connected by "if...then". It provides examples of writing the converse, inverse, and contrapositive of conditional statements. The key points are: - A conditional statement has two parts: a hypothesis and conclusion connected by "if...then" - The converse switches the hypothesis and conclusion - The inverse negates both the hypothesis and conclusion - A statement is equivalent to its contrapositive

1. 2.1 Conditional Statements Objectives: - Recognize and analyze a conditional statement - Write postulates about points, lines, & planes using conditional statements

2. Recognizing Conditional Statements If the caf is serving french fries Then I will buy some for lunch If I do my homework Then I will pass Geometry If the digits of a number add up to a number divisible by 3 Then the original number is divisible by 3

3. Recognizing Conditional Statements A conditional statement has two parts, a hypothesis and a conclusion If hypothesis Then conclusion

4. Recognizing Conditional Statements Rewrite: Two points are collinear if they lie on the same line. If two points lie on the same line, Then they are collinear

5. Recognizing Conditional Statements Rewrite: All sharks have a boneless skeleton. If the animal is a shark, Then it has a boneless skeleton

6. Recognizing Conditional Statements Rewrite: A number divisible by 9 is also divisible by 3 If a number is divisible by 9 Then it is divisible by 3

7. Writing the Converse The converse of a conditional statement is formed by switching the hypothesis and conclusion. Statement: If you see lightning Then you hear thunder Converse: If you hear thunder Then you see lightning

8. Writing the Inverse A statement can be altered by negation . Angle A is acute. Angle A is not acute. Look at the table on page 72 . . . When you negate the hypothesis and conclusion of a conditional statement, you form the inverse. When you negate the hypothesis and conclusion of a converse of a conditional statement, you form the contrapositive.

9. Writing the Inverse When two statements are both true or both false, they are called equivalent statements. A conditional statement is equivalent to its contrapositive. The inverse and converse of an conditional statement are equivalent.

10. Example Write the inverse, converse, & contrapositive of: If it is September, then apples are ripe. Inverse: If it is not September, then apples are not ripe. Converse: If apples are ripe, then it is September. Contrapositive: If the apples are not ripe, then it is not September.

11. Try some Page 75, 1-8