Q22 - Geometry

Question

State the following statement is true or not.

 

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

Step-by-Step Solution

Answer

The statement is not always true.

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.