Hypothesis Conclusion (Geometry 1_4)

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Students learn to identify the hypothesis and the conclusion of a conditional statement, and write it's converse.

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Hypothesis Conclusion (Geometry 1_4)

  1. 1. Conditional Statements and Their Converses In mathematics, you will come across many _______________. For Example: If a number is even, then it is divisible by two. If – then statements join two statements based on a condition: A number is divisible by two only if the number is even. Therefore, if – then statements are also called __________ __________ . if-then statements conditional statements You will learn to write statements in if-then form and write the converse of the statements. What You'll Learn
  2. 2. Conditional Statements and Their Converses Conditional statements have two parts. The part following if is the _________ . hypothesis The part following then is the _________ . conclusion If a number is even, then the number is divisible by two. Hypothesis: Conclusion:
  3. 3. Conditional Statements and Their Converses Conditional statements have two parts. The part following if is the _________ . hypothesis The part following then is the _________ . conclusion If a number is even, then the number is divisible by two. a number is even the number is divisible by two. Hypothesis: Conclusion:
  4. 4. Conditional Statements and Their Converses How do you determine whether a conditional statement is true or false? If it is the 4 th of July (in the U.S.), then it is a holiday. If an animal lives in the water, then it is a fish. Why? True or False Conditional Statement
  5. 5. Conditional Statements and Their Converses How do you determine whether a conditional statement is true or false? If it is the 4 th of July (in the U.S.), then it is a holiday. True The statement is true because the conclusion follows from the hypothesis. If an animal lives in the water, then it is a fish. Why? True or False Conditional Statement
  6. 6. Conditional Statements and Their Converses How do you determine whether a conditional statement is true or false? If it is the 4 th of July (in the U.S.), then it is a holiday. True The statement is true because the conclusion follows from the hypothesis. If an animal lives in the water, then it is a fish. False You can show that the statement is false by giving one counterexample . Whales live in water, but whales are mammals, not fish. Why? True or False Conditional Statement
  7. 7. Conditional Statements and Their Converses There are different ways to express a conditional statement. The following statements all have the same meaning. <ul><li>If you are a member of Congress, then you are a U.S. citizen. </li></ul><ul><li>All members of Congress are U.S. citizens. </li></ul><ul><li>You are a U.S. citizen if you are a member of Congress. </li></ul>
  8. 8. Conditional Statements and Their Converses There are different ways to express a conditional statement. The following statements all have the same meaning. <ul><li>If you are a member of Congress, then you are a U.S. citizen. </li></ul><ul><li>All members of Congress are U.S. citizens. </li></ul><ul><li>You are a U.S. citizen if you are a member of Congress. </li></ul>You write two other forms of this statement: “If two lines are parallel, then they never intersect.”
  9. 9. Conditional Statements and Their Converses There are different ways to express a conditional statement. The following statements all have the same meaning. <ul><li>If you are a member of Congress, then you are a U.S. citizen. </li></ul><ul><li>All members of Congress are U.S. citizens. </li></ul><ul><li>You are a U.S. citizen if you are a member of Congress. </li></ul>You write two other forms of this statement: “If two lines are parallel, then they never intersect.” <ul><li>All parallel lines never intersect. </li></ul><ul><li>Lines never intersect if they are parallel. </li></ul>Possible answers:
  10. 10. Conditional Statements and Their Converses The ________ of a conditional statement if formed by exchanging the hypothesis and the conclusion. converse Conditional: If a figure is a triangle , then it has three angles . Converse: If _______________, then ________________.
  11. 11. Conditional Statements and Their Converses The ________ of a conditional statement if formed by exchanging the hypothesis and the conclusion. converse Conditional: If a figure is a triangle , then it has three angles . a figure is a triangle it has three angles Converse: If _______________, then ________________.
  12. 12. Conditional Statements and Their Converses The ________ of a conditional statement if formed by exchanging the hypothesis and the conclusion. converse Conditional: If a figure is a triangle , then it has three angles . a figure is a triangle it has three angles NOTE: You often have to change the wording slightly so that the converse reads smoothly. a figure is a triangle it has three angles Converse: If _______________, then ________________.
  13. 13. Conditional Statements and Their Converses The ________ of a conditional statement if formed by exchanging the hypothesis and the conclusion. converse Conditional: If a figure is a triangle , then it has three angles . a figure is a triangle it has three angles NOTE: You often have to change the wording slightly so that the converse reads smoothly. Converse: If the figure has three angles , then it is a triangle . a figure is a triangle it has three angles Converse: If _______________, then ________________.
  14. 14. Conditional Statements and Their Converses Write the converse of the following statements. State whether the converse is TRUE or FALSE. If FALSE, give a counterexample: “ If you are at least 16 years old, then you can get a driver’s license.”
  15. 15. Conditional Statements and Their Converses Write the converse of the following statements. State whether the converse is TRUE or FALSE. If FALSE, give a counterexample: “ If you are at least 16 years old, then you can get a driver’s license.” If ________________________, then _______________________. you can get a driver’s license you are at least 16 years old
  16. 16. Conditional Statements and Their Converses Write the converse of the following statements. State whether the converse is TRUE or FALSE. If FALSE, give a counterexample: “ If you are at least 16 years old, then you can get a driver’s license.” If ________________________, then _______________________. you can get a driver’s license you are at least 16 years old TRUE!
  17. 17. Conditional Statements and Their Converses Write the converse of the following statements. State whether the converse is TRUE or FALSE. If FALSE, give a counterexample: “ If you are at least 16 years old, then you can get a driver’s license.” If ________________________, then _______________________. you can get a driver’s license you are at least 16 years old “ If today is Saturday, then there is no school. TRUE!
  18. 18. Conditional Statements and Their Converses Write the converse of the following statements. State whether the converse is TRUE or FALSE. If FALSE, give a counterexample: “ If you are at least 16 years old, then you can get a driver’s license.” If ________________________, then _______________________. you can get a driver’s license you are at least 16 years old “ If today is Saturday, then there is no school. If _______________, then ______________. there is no school today is Saturday TRUE!
  19. 19. Conditional Statements and Their Converses Write the converse of the following statements. State whether the converse is TRUE or FALSE. If FALSE, give a counterexample: “ If you are at least 16 years old, then you can get a driver’s license.” If ________________________, then _______________________. you can get a driver’s license you are at least 16 years old “ If today is Saturday, then there is no school. If _______________, then ______________. there is no school today is Saturday TRUE! FALSE!
  20. 20. Conditional Statements and Their Converses Write the converse of the following statements. State whether the converse is TRUE or FALSE. If FALSE, give a counterexample: “ If you are at least 16 years old, then you can get a driver’s license.” If ________________________, then _______________________. you can get a driver’s license you are at least 16 years old “ If today is Saturday, then there is no school. If _______________, then ______________. there is no school today is Saturday TRUE! FALSE! We don’t have school on New Years day which may fall on a Monday.
  21. 21. Conditional Statements and Their Converses End of Lesson

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