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Geom 2point1

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  • 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