Answer
To prove that $\angle B\cong\angle E$, we would use the theorem that the total sum of 3 angles in any triangles equals $180^{\circ}$.
Work Step by Step
We know the sum of 3 angles in any triangles equals $180^{\circ}$.
Therefore, $\angle A+\angle B+\angle C=\angle D+\angle E+\angle F=180^{\circ}$
So, $\angle A+ \angle B+ \angle C\cong\angle D+\angle E+ \angle F$
But, we already know that $\angle A\cong\angle D$ and $\angle C\cong\angle F$.
Therefore, it follows that $\angle B\cong\angle E$
In conclusion, to prove that $\angle B\cong\angle E$, we would use the theorem that the total sum of 3 angles in any triangles equals $180^{\circ}$.
