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.
Find a Pattern: 1+2=3 3+3=6 6+4=10So the numbers increase by 2, 3 and 4.
Counter Example• An example used to show that a given statement is not always true.
Find a Counter Example1. Given: DE = EF Conjecture: E is the midpoint of DF Answer: True, there is no counter example.
Find a Counter Example2. Given: JK = KL = LM = MJ Conjecture: JKLM forms a square Answer: JKLM may not have all right angles.
Find a Counter Example3. Given: n is a real number Conjecture: n x n is nonnegative number Answer: True, there is no counter example.
As you can see you cannot alwaysfind a counter example, but when you do they prove the conjecture/statement false.