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# Geom 2point1

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### Geom 2point1

1. 1. 2.1 Conditional Statements Objectives: - Recognize and analyze a conditional statement - Write postulates about points, lines, & planes using conditional statements
2. 2. Recognizing Conditional Statements <ul><li>If the caf is serving french fries </li></ul><ul><ul><li>Then I will buy some for lunch </li></ul></ul><ul><li>If I do my homework </li></ul><ul><ul><li>Then I will pass Geometry </li></ul></ul><ul><li>If the digits of a number add up to a number divisible by 3 </li></ul><ul><ul><li>Then the original number is divisible by 3 </li></ul></ul>
3. 3. Recognizing Conditional Statements <ul><li>A conditional statement has two parts, a hypothesis and a conclusion </li></ul><ul><li>If hypothesis </li></ul><ul><ul><li>Then conclusion </li></ul></ul>
4. 4. Recognizing Conditional Statements <ul><li>Rewrite: Two points are collinear if they lie on the same line. </li></ul><ul><li>If two points lie on the same line, </li></ul><ul><ul><li>Then they are collinear </li></ul></ul>
5. 5. Recognizing Conditional Statements <ul><li>Rewrite: All sharks have a boneless skeleton. </li></ul><ul><li>If the animal is a shark, </li></ul><ul><ul><li>Then it has a boneless skeleton </li></ul></ul>
6. 6. Recognizing Conditional Statements <ul><li>Rewrite: A number divisible by 9 is also divisible by 3 </li></ul><ul><li>If a number is divisible by 9 </li></ul><ul><ul><li>Then it is divisible by 3 </li></ul></ul>
7. 7. Writing the Converse <ul><li>The converse of a conditional statement is formed by switching the hypothesis and conclusion. </li></ul><ul><li>Statement: If you see lightning </li></ul><ul><ul><li>Then you hear thunder </li></ul></ul><ul><li>Converse: If you hear thunder </li></ul><ul><ul><li>Then you see lightning </li></ul></ul>
8. 8. Writing the Inverse <ul><li>A statement can be altered by negation . </li></ul><ul><li>Angle A is acute. </li></ul><ul><li>Angle A is not acute. </li></ul><ul><li>Look at the table on page 72 . . . </li></ul><ul><li>When you negate the hypothesis and conclusion of a conditional statement, you form the inverse. </li></ul><ul><li>When you negate the hypothesis and conclusion of a converse of a conditional statement, you form the contrapositive. </li></ul>
9. 9. Writing the Inverse <ul><li>When two statements are both true or both false, they are called equivalent statements. </li></ul><ul><li>A conditional statement is equivalent to its contrapositive. </li></ul><ul><li>The inverse and converse of an conditional statement are equivalent. </li></ul>
10. 10. Example <ul><li>Write the inverse, converse, & contrapositive of: </li></ul><ul><li>If it is September, then apples are ripe. </li></ul><ul><li>Inverse: If it is not September, then apples are not ripe. </li></ul><ul><li>Converse: If apples are ripe, then it is September. </li></ul><ul><li>Contrapositive: If the apples are not ripe, then it is not September. </li></ul>
11. 11. Try some <ul><li>Page 75, 1-8 </li></ul>
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