Given: AB ≅ CB and D is the midpoint of AC. Are these two triangles congruent? If so by what theorem?

Answer:
Option (1)
Step-by-step explanation:
From the picture attached,
In ΔADB and ΔCDB,
AB ≅ BC [Given]
BD ≅ BD [Reflexive property]
AD ≅ DC [Given] (since D is the midpoint of AC)
Therefore, ΔADB ≅ ΔCDB [By SSS postulate of congruence]
Option (1) will be the answer.