Triangle ADE is congruent to triangle CDB by the Side-Side-Side (SSS) rule when DE ≅ DB, AD ≅ CD, and AD ≅ BC.
To prove triangle ADE ≅ triangle CDB using the Side-Side-Side (SSS) rule, we need to show that all three corresponding sides of the triangles are congruent.
Given that DE ≅ DB and AD ≅ CD, we already have two pairs of congruent sides. Now, to complete the SSS criterion, we need to establish the congruence of the third pair of sides.
The correct choice is C. AD ≅ BC. If AD is congruent to BC, then we have three pairs of congruent sides: DE ≅ DB, AD ≅ CD, and AD ≅ BC. Therefore, by the SSS rule, we can conclude that triangle ADE is congruent to triangle CDB.
Options A (AE ≅ CB) and B (ED ≅ CD) do not provide sufficient information to satisfy the SSS criterion. Option D (AD ≅ BD) would make the triangles AD and DB congruent, but we need AD to be congruent to BC, not BD.
In summary, to prove triangle ADE ≅ triangle CDB using the SSS rule, we need to establish that AD ≅ BC in addition to the given congruences DE ≅ DB and AD ≅ CD.