Answer:
Step-by-step explanation:Since B is the midpoint of AC, this means that AB and BC are equal in length, as the midpoint of a line segment divides it into two equal parts.
2. Let's assume that AB is not equal to BC. In this case, one of the line segments AB or BC would be longer than the other.
3. Since EB = BC, if AB is longer than BC, then EB would be shorter than AB. But since B is the midpoint of AC, EB and BC should be equal in length.
4. Similarly, if BC is longer than AB, then EB would be longer than BC. But again, EB and BC should be equal since B is the midpoint of AC.
5. Since assuming AB is not equal to BC leads to contradictions, our assumption is false. Therefore, AB must be equal to BC.