# Inductive reasoning

##### Intros
###### Lessons
1. Inductive Reasoning Overview:
What are conjectures?
##### Examples
###### Lessons
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. $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}$
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 $a$ and line $b$ are perpendicular
4. 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:
1. Given: A = (0,0), B = (0,1), C = (1,0).
Conjecture: ABC form a right isosceles triangle.
2. Given: $a$ is a negative integer.
Conjecture: $\ a^2$ is a positive integer.
3. Given: $\overline{AB}$ and $\overline{BC}$ are parallel
Conjecture: AB = BC
4. Given: $x + y \geq 10 . x \geq 5$
Conjecture: $y \geq 6$