Question

I need help solving this with the statements and reasons

Answer 1

Given that:

`\bar{AB}\mleft\Vert \mright?\bar{DC}`

To prove that:

`\Delta ABE\cong\Delta\text{CDE}`

We know that congruent parts of congruent triangles are congruent

`\angle\text{AEB }\cong\angle CDE\text{ (vertically opposite angles)}`

Given that E is the midpoint of AC, therefore,

`\begin{gathered} EA=EC\text{ } \\ EB=ED \end{gathered}`

By the SAS congruency theorem as illustrated above, it is sufficient to prove that the triangles are congruent