Final answer:
The reason why △ABC≅△DBC is because they have congruent parts. Triangles ABB' and AA'B' share congruent segments on the surface AB'. Furthermore, triangles BAO and B₁ A₁ O are similar triangles, thus showing that △ABC≅△DBC.
Step-by-step explanation:
The reason why △ABC≅△DBC is because they have congruent parts. In Problem 1, there are congruent segments on the surface AB'. These segments are shared by both triangles ABB' inside medium 1 and AA'B' inside medium 2.
Additionally, triangles BAO and B₁ A₁ O are similar triangles, which means they have the same shape but possibly different sizes. When we compare the corresponding sides of these triangles, we find that they are proportionate. This similarity proves that △ABC≅△DBC.