a)
The single marks on each angle shows that the angles are congruent. This means that angle CBD and angle angle ABD are congruent.
Also, line BC is common to both traingle ABD and CBD. This means that it is congruent for both triangles.
If both angles are congruent, then and line AC is a straight segment, it means that line AB is congruent to line CB. Thus, we have two congruent lines and one congruent angle. Therefore,
Triangle CBD is congruent to triangle ABD
The congruence statement is Side Angle Side(SAS)