Jump Start: October 5, 2009

1. Jump Start: October 5, 2009 Draw a conclusion from the following statements. If it is raining, the temperature is greater than 32° F. If the temperature is greater than 32°F, then it is not freezing outside. It is raining.

2. Homework Answers pg. 85 #11 – 15 11. If two planes are not parallel, then they intersect in a line. 12. If you read a good book, then you time is well spent. 13. If you are studying botany, then you are studying a science. 14. If an Alaskan mountain is over 20,300 ft high, then it is the highest in the United States. Alaska’s Mt. McKinley is the highest in the United States. (answers will vary) 15. If you live in Little Rock, then you live in the 25th state to enter the Union. Levon lives in the 25th state to enter the Union. (answers will vary)

3. REVIEW If two figures are congruent, their areas are equal. • What is the hypothesis in the conditional statement above? If two figures are congruent • What is the conclusion in the conditional statement above? Their areas are equal • What is the converse of the conditional statement? If their areas are congruent, then the two figures are congruent.

4. REVIEW If the car is full of gas, then the engine will start. • What is the truth value of the conditional statement above? Justify! False; battery could be dead. • What is the truth value of the converse of the conditional statement above? Justify False; Car could have a half tank of gas.

5. REVIEW If shoes can fly, winter is cold. • What is the truth value of the conditional statement above? Vacuously True • What is another vacuously true conditional statement? • What is another vacuously true conditional statement?

6. REVIEW A whole number is a multiple of 5 if and only if its last digit is either a 0 or a 5. • What kind of statement is written above? biconditional • What are the two conditional statements that make up the biconditional statement above? If a whole number is a multiple of 5, then its last digit is either 0 or 5. If a whole numbers has a last digit of 0 or 5, then it is a multiple of 5. • Is the biconditional above a good definition? Explain Yes; both conditional statements are true!

7. Is it possible to use the Law of Detachment? If so, write the conclusion. If not, write not possible. REVIEW • If you live in Chicago then you live in Illinois. • Brad lives in Illinois. Not Possible • If two planes do not intersect, then they are parallel. • Plane ABCD and Plane EFGH do not intersect. Plane ABCD and Plane EFGH are parallel

8. REVIEW Use the Law of Syllogism to draw a conclusion. • If a polygon is a hexagon, then the sum of its angles is 720. • If the sum of the angles of a polygon is 720, then it has six sides. If a polygon is a hexagon, then it has six sides. • If two lines are not parallel, then they intersect. • If two lines intersect, then they intersect at a point. If two lines are not parallel, then they intersect at a point.

9. Alternate Assignment • Chapter 2 Chapter Test • Pg. 109 #1 – 9, 22 – 26

10. Homework • Chapter 2 Review (pg. 105 – 106) • #11 – 23 ALL • STUDY!!!

11. Mid-Chapter 2 Test Review Conditionals Converses Biconditionals Definitions Detachment Syllogism Misc. 100 100 100 100 100 100 100 200 200 200 200 200 200 200 300 300 300 300 300 300 300 400 400 400 400 400 400 400 500 500 500 500 500 500 500

12. Conditionals ~ 100 Points Write the statement as a conditional. All babies are cute.

13. Conditionals ~ 100 Points Answer If it is a baby, then it is cute. Back

14. Conditionals ~ 200 Points What are the two parts that make up a conditional statement?

15. Conditionals ~ 200 Points Hypothesis and Conclusion Answer Back

16. Conditionals ~ 300 Points Show that the conditional statement is false by finding a counterexample. If it is not January, then it must be June.

17. Conditionals ~ 300 Points Answer Any month other than January and June. Back

18. Conditionals ~ 400 Points What is wrong with the conditional statement below? Fix it! I will win, if I play CASH 4 today!

19. Conditionals ~ 400 Points Answer Not in the order: “If (hypothesis), then (conclusion).” Correction: If I play CASH 4 today, then I will win! Back

20. Conditionals ~ 500 Points Find the truth value of the conditional statement:

21. Conditionals ~ 500 Points Answer Vacuously True Back

22. Converses ~ 100 Points Write the converse: If you do not sleep, then you will be tired.

23. Converses ~ 100 Points Answer • If you are tired, then you did not sleep. Back

24. Converses ~ 200 Points Write the converse: If a rectangle has four sides the same length, Then it is a square.

25. Converses ~ 200 Points If it is a square, then it is a rectangle that has four sides the same length. Answer Back

26. DAILY DOUBLE

27. Converses ~ 600 Points Find the truth value of the converse. If true, prove. If false, provide counterexample. If you are a teenager, then you are younger than 20.

28. Converses ~ 600 Points Answer FALSE, Age 0 - 12 Back

29. Converses ~ 400 Points • Find the truth value of the converse. • If true, prove. If false, provide counterexample. If y = 3, then 2y – 1 = 5.

30. Converses ~ 400 Points Answer TRUE, 2(y) – 1 = 6 – 1 = 5 Back

31. Converses ~ 500 Points • Find the truth value of the converse. • If true, prove. If false, provide counterexample. If m2 is positive, then m is positive.

32. Converses ~ 500 Points Answer • TRUE, you can’t get a negative number out of a square. Back

33. Biconditionals ~ 100 Points • What is a biconditional statement?

34. Biconditionals ~ 100 Points Answer • A conditional statement that is true and whose converse is true Back

35. Biconditionals ~ 200 Points • What is another name for a biconditional statement?

36. Biconditionals ~ 200 Points Answer “If and only if” Statement Back

37. Biconditionals ~ 300 Points • Break the biconditional statement into 2 conditional statements: A figure has eight sides if and only if it is an octagon.

38. Biconditionals ~ 300 Points • If it is an octagon, then it has eight sides. • If it has eight sides, then it is an octagon. Answer Back

39. Biconditionals ~ 400 Points Break the biconditional statement into 2 conditional statements: You live in Texas if and only if you live in the largest state in the contiguous US.

40. Biconditionals ~ 400 Points Answer • If you live in Texas, then you live in the largest state in the contiguous US. • If you live in the largest state in the contiguous US, then you live in Texas. Back

41. Biconditionals ~ 500 Points • Come up with a biconditional statement and the two conditional statements that form it.

42. Biconditionals ~ 500 Points Answer Biconditional: Hypothesis if and only if conclusion. Conditional: If hypothesis, then conclusion. Conditional: If conclusion, then hypothesis. Back

43. Definitions ~ 100 Points • What is a good definition?

44. Definitions ~ 100 Points Answer • A definition that can be written as a biconditional. Back

45. Definitions ~ 200 Points Is the definition a good definition? Prove it! Collinear points are points that lie on the same line.

46. Definitions ~ 200 Points Yes, it is biconditional. Both the conditional and the converse are true. Answer Back

47. Definitions ~ 300 Points Is the definition a good definition? Prove it! Congruent angles are angles with equal measure.

48. Definitions ~ 300 Points Yes, it is biconditional. Both the conditional and the converse are true. Answer Back

49. Definitions ~ 400 Points Is the definition a good definition? Prove it! A car is a motorized vehicle with 4 wheels.

50. Definitions ~ 400 Points Answer • No, not biconditional. The converse is false. (Truck, etc.) Back