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.