Question

Given ΔAEC≌ ΔAFC and angle B ≌ angle D. Prove ΔEBC ≌ ΔFDC

Answer 1

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.

`\text{angle supp. to AEC }=180^(\circ)-AEC\cong180-AFC=\text{ angle supp. to AFC}`

Also, it has already been shown that:

`\begin{gathered} \text{angle supp. to AEC }=\text{ BEC} \\ \\ \text{angle supp. to AFC }=\text{DFC} \end{gathered}`

Therefore:

`\text{BEC}\cong\text{ DFC}`