Given that:
[tex]\bar{AB}\mleft\Vert \mright?\bar{DC}[/tex]
To prove that:
[tex]\Delta ABE\cong\Delta\text{CDE}[/tex]
We know that congruent parts of congruent triangles are congruent
[tex]\angle\text{AEB }\cong\angle CDE\text{ (vertically opposite angles)}[/tex]
Given that E is the midpoint of AC, therefore,
[tex]\begin{gathered} EA=EC\text{ } \\ EB=ED \end{gathered}[/tex]
By the SAS congruency theorem as illustrated above, it is sufficient to prove that the triangles are congruent
