Question

ad ≅ cd
reason:
select reason
ab ≅ cb
reason:
select reason
bd ≅ bd
reason:
select reason
△abd ≅ △cbd
reason:
select reason

Explanation:

Step1: For $\overline{AD}\cong\overline{CD}$

Given (assuming this is provided information in the problem - context).

Step2: For $\overline{AB}\cong\overline{CB}$

Given (assuming this is provided information in the problem - context).

Step3: For $\overline{BD}\cong\overline{BD}$

Reflexive property of congruence (a segment is congruent to itself).

Step4: For $\triangle ABD\cong\triangle CBD$

Side - Side - Side (SSS) congruence criterion (since we have $\overline{AD}\cong\overline{CD}$, $\overline{AB}\cong\overline{CB}$ and $\overline{BD}\cong\overline{BD}$).

Answer:

$\overline{AD}\cong\overline{CD}$ - Given; $\overline{AB}\cong\overline{CB}$ - Given; $\overline{BD}\cong\overline{BD}$ - Reflexive property of congruence; $\triangle ABD\cong\triangle CBD$ - SSS congruence criterion.