It has already been shown that angles AEC and AFC are congruent.
Then, the angle that is supplementary to AEC and the angle supplementary to AFC are also congruent.
[tex]\text{angle supp. to AEC }=180^{\circ}-AEC\cong180-AFC=\text{ angle supp. to AFC}[/tex]
Also, it has already been shown that:
[tex]\begin{gathered} \text{angle supp. to AEC }=\text{ BEC} \\ \\ \text{angle supp. to AFC }=\text{DFC} \end{gathered}[/tex]
Therefore:
[tex]\text{BEC}\cong\text{ DFC}[/tex]
