In order to prove that the triangles are congruent, we can use the following statements and reasons:
2.
Statement: Angles ADB and DBC are congruent.
Reason: Alternate interior angles.
3.
Statement: Angles CDB and DBA are congruent.
Reason: Alternate interior angles.
4.
Statement: segment BD is congruent to segment BD.
Reason: Reflexive property of equality.
5.
Statement: Triangle ABD congruent to triangle CDB.
Reason: ASA case of congruency.