Answer: Congruency can not be proved with the information provided
Why not? Because the SSA rule isn't a valid congruence theorem.
BC = BC is the shared segment along the vertical.
The tickmarks tell us that AC = CD is another pair of congruent sides.
Those form the two "S" of SSA.
The "A" refers to angle BAC = angle BDC. Pay careful attention to the fact these angles are not between the congruent sides. If we knew that angle ACB = angle BCD, then we could use the SAS congruence theorem. However, we don't have this info and we have SSA instead.
SSA isn't valid because it could lead to triangle ambiguity.
We cannot use ASA or AAS because we only have info about one pair of angles. We cannot use SSS because we don't have info about all 3 pairs of sides.