Answer:
In a general context (because there's no specific data in the problem), we could demonstrate the similarity using one of the postulates. Specifically, we could use the Angle-Angle postulate.
We have a triangle ABC, and inside of it there's a line that crosses to sides, and its parallel to the third side. This set-up gives us parallels that are being intersected by transversal, this means that all angles are congruent between the triangle ABC and the new triangle DBE.
Basically, they share the same upside angle, and the other two at their base are also congruent because they are corresponding angles.
Therefore, by AA postulate, both triangles are similar.