Inductive reasoning

Lessons

• Introduction
  Inductive Reasoning Overview:
  a)

  What are conjectures?
  
  

---

• 1.
  Making a Conjecture

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

  a)

  1, 3, 5, 7, 9,…
  
  
  b)

  $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}$
  
  
  c)

  
  
  
  d)

  
  
  
  e)

  
  
  
  f)

  
  
  

---

• 2.
  Make a conjecture with the given information. Draw a figure to show that your conjecture is correct:
  a)

  ABC is a triangle and AB = BC
  
  
  b)

  ABC is a triangle and $\angle$B is a right angle.
  
  
  c)

  Line $a$ and line $b$ are perpendicular
  
  
  d)

  Line $a$ and line $b$ 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:
  a)

  Given: A = (0,0), B = (0,1), C = (1,0).
  Conjecture: ABC form a right isosceles triangle.
  
  
  b)

  Given: $a$ is a negative integer.
  Conjecture: $\ a^2$ is a positive integer.
  
  
  c)

  Given: $\overline{AB}$ and $\overline{BC}$ are parallel
  Conjecture: AB = BC
  
  
  d)

  Given: $x + y \geq 10 . x \geq 5$
  Conjecture: $y \geq 6$
  
  

---