Question

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

If $\angle BEC\cong \angle CEF$, then$\overrightarrow{EC}$ is the bisector of $\angle BEF$ .

Short answer

The angle bisector 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 the point E. $\overrightarrow{EC}$ bisects $\angle BEF$.

Step 2. State the angle bisector theorem.

The relative lengths of the two parts in which the side of a triangle is separated by a line bisecting the opposite angle. This equates their relative lengths with the relative lengths of the triangle's other two sides.

Step 3. State the conclusion

Considering the given diagram and the statement that if $\angle BEC\cong \angle CEF$, then $\overrightarrow{EC}$is the bisector $\angle BEF$.

Therefore, the statement about the diagram is justified by the angle bisector theorem.