Question

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

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

Short answer

The midpoint theorem 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 point E.

Step 2. State the midpoint theorem.

The theorem states that the line segment formed by joining the midpoints of the two sides of a triangle is parallel and also half of the length of the third side of the triangle.

Step 3. State the conclusion.

As $\overline{EB}$bisects $\overline{AF}$ at the point E, so, E is the midpoint of $\overline{AF}$.

Therefore, the statement about the diagram is justified by the midpoint theorem.