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Daily-Quiz (Monday) 9/9

Daily-Quiz (Monday) 9/9. M is the midpoint of . L has coordinates (7, -4) and M has coordinates (1, -8). Find the coordinates of N. Daily-Quiz (Tuesday) 9/10. Find the coordinates of the midpoint of the segment. with A(-2,3) and B(4,1). Daily-Quiz ( Wed ) 9/11.

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Daily-Quiz (Monday) 9/9

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  1. Daily-Quiz (Monday) 9/9 M is the midpoint of . L has coordinates (7, -4) and M has coordinates (1, -8). Find the coordinates of N.

  2. Daily-Quiz (Tuesday) 9/10 Find the coordinates of the midpoint of the segment. with A(-2,3) and B(4,1).

  3. Daily-Quiz (Wed) 9/11 Multiply the previous number by 4 1280, 5120, 20480

  4. Daily-Quiz (Thurs.) 9/12 3, 9, 27

  5. 2.1 Using Inductive Reasoning to make conjectures Learning Objective: SWBAT Use inductive reasoning to identify patterns and make conjectures. Find counterexamples to disprove conjectures.

  6. KEY TERMS: Conjecture – is an unproven statement that is based on observation. Example: If yesterday was Monday and today is Tuesday tomorrow is ________.

  7. KEY TERMS: Inductive Reasoning – process of recognizing or observing a pattern and drawing conclusion. Example #1:

  8. Example#2: Describe the pattern in the numbers -1, -4, -16, -64, …Write the next 3 numbers in the pattern. -256, -1024, -4096

  9. Make a Conjecture Example#3: Given 5 noncollinear points, make a conjecture about the # of ways to connect different pairs of the points. Make a table and look for a pattern. 0 1 3 6 10 4 1 2 3 6+4 10

  10. KEY TERMS: Counterexample – Is a specific case for which the conjecture is false.

  11. Example #4: A student makes the following conjecture about the sum of two #’s. Find a counterexample to disprove the students conjecture. Conjecture: The sum of two #’s is always greater than the larger number.

  12. Example #4: Conjecture: The sum of two #’s is always greater than the larger number. 1 + 2 = 3 3 > 2 True -3 + -4 = -7 -7 -4 False Is this true for all positive integers? So, because a counterexample exist the conjecture is false.

  13. Example #5: (you try) Find a counterexample to show that the following conjecture is false. Conjecture: The value of is always greater than the value of x. > > 4 > 2 True .25 .50 False So, because a counterexample exist the conjecture is false.

  14. Example #6: Find a counterexample to show that the following conjecture is false. Conjecture: The product is equal to , for = + Counterexample: = 5 False So, because a counterexample exist the conjecture is false.

  15. Example #7: Find a counterexample to show that the following conjecture is false. Conjecture: The difference of 2 positive #’s is always a positive #. Counterexample: 10 – 4 = 6 True False So, because a counterexample exist the conjecture is false.

  16. Example #8: Find a counterexample to show that the following conjecture is false. Given: AB + BC = AC Conjecture: AB = BC Counterexample: So, because a counterexample exist the conjecture is false.

  17. Assignment 2.1 Worksheet pg. 15 Front & back

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