Inductive reasoning

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  1. Inductive Reasoning Overview:
    What are conjectures?
  1. Making a Conjecture

    Make a conjecture of the next item or number based on the information given:

    1. 1, 3, 5, 7, 9,…
    2. 12,13,14,15\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}
    3. ex 1c
    4. ex 1d
    5. ex 1e
    6. ex 1f
  2. Make a conjecture with the given information. Draw a figure to show that your conjecture is correct:
    1. ABC is a triangle and AB = BC
    2. ABC is a triangle and \angle B is a right angle.
    3. Line a a and line b b are perpendicular
    4. Line a a and line b b are parallel
  3. Counterexamples of Conjectures
    Determine if the following conjecture is true or false. If it is false, then find a counterexample of the conjecture:
    1. Given: A = (0,0), B = (0,1), C = (1,0).
      Conjecture: ABC form a right isosceles triangle.
    2. Given: a a is a negative integer.
      Conjecture:  a2\ a^2 is a positive integer.
    3. Given: AB \overline{AB} and BC \overline{BC} are parallel
      Conjecture: AB = BC
    4. Given: x+y10.x5 x + y \geq 10 . x \geq 5
      Conjecture: y6 y \geq 6