One way to prove that the triangles are congruent is to show that the three pairs of sides have the same length.
For side [tex]BD[/tex], this is easy, since it is shared by the two triangles, so it is obviously equal.
On the other hand, we know that the given figure is a parallelogram, the opposite sides are equal in length. Particularly, it means that:
[tex]AB = CD \quad\textrm{and}\quad BC = AD.[/tex]
Thus, we have shown that each pair of sides have the same length, which means that:
[tex]\triangle ABD \equiv \triangle CDB.[/tex]
