[tex]\begin{gathered} EB\text{ is the perpendicular bisector of AD} \\ AB=BD\to\text{This is correct} \\ \angle BEC\cong\angle DEC\to(\text{ This is incorrect)} \\ \text{There are no enough information to conclude }\angle BEC\cong\angle DEC \\ \text{Besides the student states:} \\ BC=CD \\ \text{The diagram doesn't tell anything about segment EC, he can't } \\ \text{conclude EC is a bisector of BD} \end{gathered}[/tex]
