1. Inductive Reasoning and Conjecture “Proofs”

2. Definition Conjecture Educated Guess!!!  Inductive Reasoning Steps you take to make your guess

3. Examples: Brenda has just gotten a job as the plumber’s assistant. Her first task is to open all the water valves to release the pressure on the lines. The first four valves she discovered opened when turning counterclockwise… What is her conjecture? All valves will be open by turning them counterclockwise

4. Examples: Eric was driving his friend to school when his car suddenly stopped two blocks away from school… What is his conjecture? The car run out of gas The battery cable lost its contact

5. Example: For points A, B and C, AB = 10, BC = 8 and AC = 5… Summarize: Given : Points A, B and C AB = 10, BC= 8, AC = 5 What is our conjecture? Points A, B and C are noncollinear (not on the same line)

6. Examples Given ∠ 1 and ∠ 2 are supplementary ∠ 1 and ∠ 3 are supplementary What is our conjecture? ∠ 2 = ∠ 3

7. Counterexamples: Sometimes after we make a conjecture, we realize that the conjecture is FALSE. Its takes only one false example to show that a conjecture is NOT TRUE. The false example is called: Counterexample.

8. Counterexample: Points P, Q and W are collinear. Joe made a conjecture that Q is between P and W. Determine if this conjecture is true or false? Given: Points P, Q and W are collinear  Joe’s Conjecture: Q is between P and R  Solution: False, PW Q 

9. Counterexample: Determine of the conjecture is true of false? Given : FG = GH Conjecture: G is a midpoint of FH Is this statement TRUE or FALSE? Remember one example needed to show FALSE Solution: False,    F G H G is NOT a midpoint, G is a vertex

10. More Examples: Determine if this conjecture is TRUE or FALSE based on the given information. Given : Collinear Points D, E and F Conjecture: DE + EF = DF Solution: FALSE, FED 

11. More Examples: Determine if this conjecture is TRUE or FALSE based on the given information. Given : ∠ A and ∠ B are supplementary Conjecture: ∠ A and ∠ B are adjacent Conclusion: FALSE, ∠ A= 30 ∠ B= 150

14. Practice