Suppose that EB and DC are parallel; therefore, triangles EAB and DAC are similar triangles due to the AAA postulate. Because those two triangles are similar, the ratio between their corresponding sides is constant; then,
[tex]\frac{EA}{DA}=\frac{BA}{CA}[/tex]
Thus,
[tex]\begin{gathered} \Rightarrow\frac{8}{6+8}=\frac{6.5}{5+6.5} \\ \Rightarrow\frac{8}{14}=\frac{6.5}{11.5} \\ \Rightarrow0.571428\ldots=0.565217\ldots!!! \end{gathered}[/tex]
The two quantities are not the same, this is a contradiction. Thus, EB and DC cannot be parallel.
