Before making a two-column proof, let's see what information is given to use.
Given: △ EAB ≅ △ DCB
Next, let's mark the corresponding congruent parts in the given diagram.
From the diagram above we get EA ≅ CD. Also, AB ≅ CB and BD ≅ BE, which implies that AB = CB and BD = BE. Let's add these two equations.
AB &= CB
^+ BD &= BE
AB+ BD &= CB+ BE
Applying the Segment Addition Postulate to the equation above we get AD=CE, which implies that AD ≅ CE. Finally, let's separate the two triangles △ EAD and △ DCE.
As we can see, both triangles share the side ED, and by the Reflexive Property of Congruent Segments we get ED ≅ ED. Thus, we can apply the Side-Side-Side (SSS) Congruence Postulate to conclude that △ EAD ≅ △ DCE. We will summarize the proof in the following table.
