Transcript Inductive Reasoning and Conjecture

Inductive Reasoning
and Conjecture
Section 2-1
Objective: Find counterexamples
Conjecture
An educated guess based on known
information.
Inductive Reasoning
Reasoning that uses a number of specific
examples to arrive at a conjecture.
Example of Inductive Reasoning
The last five mornings I drove to Auburn,
the traffic was heavy on Wednesdays
and light on Sundays.
Conclusion: Weekdays have heavier
traffic than weekends.
Example 1
Finding a Pattern using Inductive
Reasoning

Make a conjecture about the next
triangular number.
Example 2
Make a conjecture about the next
number.
-8, -5, -2, 1, 4, ____
Practice 1
Make a conjecture about the next number
in the sequence.
1. 1, 2, 4, 8, 16, ____
2. 4, 6, 9, 13, 18, _____
3. 1/2, 1/4, 1/8, 1/16, ____
Example 3
Make a conjecture. Draw an example to
support your conjecture.
1.
For points P, Q, and R, PQ = 9,
QR = 15, and PR = 12.
Example 3
2.
< 3 and < 4 are a linear pair.
Example 3
3.
The sum of two odd numbers.
Practice 2
1.
The sum of two even numbers.
2.
The relationship between AB and EF if
AB = CD and CD = EF.
3.
The sum of squares of two
consecutive natural numbers.
Counterexample
One case that the conjecture does not
work. Proves a conjecture wrong.
Example 4
Determine whether each is true or false.
Give a counterexample for a false
statement.
1.
If n is a real number, then n2 > n
Example 4
2.
If JK = KL, then K is the midpoint of JL
Example 4
3.
If n is a real number, then –n is a
negative number.
Practice 3
Determine whether each is true or false.
Give a counterexample for a false
statement.
1. If <ABC = <DBE, then <ABC and <DBE are
vertical angles.
2. If <A and <B are supplementary, then they
share a side.
3. If <1 and <2 are adjacent angles, then <1
and <2 form a linear pair.