1. Chapter 2 Section 1
Miss Novak

2. Conjecture
• An educated guess based
on known information.

3. Inductive
Reasoning
• Reasoning that uses a
number of specific examples
to arrive at a plausible
generalization or prediction

4. Patterns and
Conjectures

5. Give it a try!
• The numbers represented below are called
triangular numbers. Make a conjecture about
the next triangular number based on the
pattern.
Observe: Each triangle is formed by adding
another row of dots.

6. Find a Pattern: 1+2=3 3+3=6 6+4=10
So the numbers increase by 2, 3 and 4.

7. Counter Example
• An example used to show that a
given statement is not always true.

8. Find a Counter Example
1. Given: DE = EF
Conjecture: E is the midpoint of DF
Answer: True, there is no counter example.

9. Find a Counter Example
2. Given: JK = KL = LM = MJ
Conjecture: JKLM forms a square
Answer: JKLM may not have all right angles.

10. Find a Counter Example
3. Given: n is a real number
Conjecture: n x n is nonnegative number
Answer: True, there is no counter example.

11. As you can see you cannot always
find a counter example, but when
you do they prove the
conjecture/statement false.

12. Homework
Chapter 2 Section 1
#1-17 odd
#29-37 odd