Question

State the following statement is true or not.

If $AB=BC$, then point B must be the midpoint of $\overline{AC}$.

Short answer

The statement is not always true.

Step-by-step solution

Step 1. Check the figures.

Step 2. Step description.

For the first figure, A, B, and C are collinear.

So, the statement is true when A, B, and C are collinear.

Thus, if $AB=BC$ then point B must be the midpoint of $\overline{AC}$if A, B, and C are collinear.

Step 3. Step description.

For the second figure, if $AB=BC$, then M is the midpoint.

Thus, the statement is not true for the second figure.

Therefore, the statement is not always true.