In the given figure we have the following:
Statement
[tex]\Delta ABD\cong\Delta CBD[/tex]
This means that triangle ABD is congruent with triangle CDB.
Reason:
Since BD = BS and we have that:
[tex]\begin{gathered} \angle ABD=\angle CBD \\ \angle\text{ADC}=\angle CDB \end{gathered}[/tex]
We can apply the ASA (Angle Side Angle) theorem of congruency.
