Question

which postulate or theorem can be used to prove that BCD is similar to EFG?(will send a picture example)

Answer 1

Two triangles are similar if all their corresponding angles are congruent and their corresponding sides are proportional.

If all sides are proportional, that is enough information to know that the triangles are similar.

As we know all the side lengths of both triangles, we can find three pair of corresponding sides. The postulate that correspond is SSS Similarity theorem (SSS: side-side-side).