Triangles A B C and A D C share common side A C. The lengths of A B and A D are congruent.

To determine whether triangles ABC and ADC can be congruent by the SSS (Side-Side-Side) criterion, we need to analyze the information given.

1. The triangles share a common side AC.
2. The lengths AB and AD are congruent (AB ≅ AD).

For triangles to be congruent by SSS, all three sides of one triangle must be equal to all three sides of the other triangle. Therefore, we need to check if we have three pairs of corresponding sides that are congruent between ΔABC and ΔADC.

The sides we have are:

• AC is common to both triangles.
• AB ≅ AD by the given information.
• We do not know the length of BC or DC, hence we cannot directly conclude about them.

However, for ΔABC to be congruent to ΔADC:

1. We would need AB ≅ AD (this is given).
2. We would need AC ≅ AC (this is trivially true as it's a shared side).
3. We would need BC to be congruent to DC (BC ≅ DC).

The statement "ΔABC could be congruent to ΔADC by SSS" would only be true if BC ≅ DC, since we already have one pair of congruent sides (AB ≅ AD) and the common side (AC).

Thus, the correct answer would be: Yes, but only if BC ≅ DC.

So, the option that fits is: Yes, but only if BC ≅ DC.