Answer:
First of all, let's define what counterexample means. This is an example that disproves an statement. In this exercise, our statement is:
- If [tex]\overline{AB}=\overline{BC}[/tex] then [tex]B[/tex] is the midpoint of [tex]\overline{AC}[/tex]
Since the problem allows us to use words or a diagram, let's use a diagram in order to prove it. The Figure 1 below shows our statement. As you can see, the statement is fulfilled in this diagram because [tex]\overline{AB}=\overline{BC}[/tex], then [tex]B[/tex] is the midpoint of [tex]\overline{AC}[/tex], but this is true because these three points are collinear, that is, they line on the same line. However, if those points aren't collinear, the statement can be disproved. This is shown in the second figure where ∠B is 90°. So if you get an angle ∠B different from 180°, the statement is false.
