Question

State which postulate, definition, or theorem justifies the statement about the diagram.

If E is the midpoint of $\overline{AF}$, then $\overline{EC}$, bisects $\overline{AF}$ .

Short answer

The fact that the midpoint of a line divides it into equal parts justifies the statement about the diagram.

Step-by-step solution

Step 1. Observe the given diagram.

The diagram constitutes a straight-line AEF and two other lines meet the line AEF at the point E. E is the midpoint of AF.

Step 2. State the midpoint theorem.

The theorem states that if E is the midpoint of AF, then AE is equal to EF.

Step 3. State the conclusion.

As E is the midpoint of $\overline{AF}$, then any line passing through E also bisects $\overline{AF}$,

Since the line $\overline{EC}$ passes through the point E, then $\overline{EC}$ bisects $\overline{AF}$.

Therefore, the statement about the diagram is justified by the reason that the midpoint of a line divides it into equal parts.