Question

ac⊥bd
reason: given
∠adb and ∠cdb are right angles
reason: perpendicular lines form right angles
∠adb≅∠cdb
reason:
∠abd≅∠cbd
reason:
bd≅bd
reason:
△abd≅△cbd
reason:

Explanation:

Answer:

$\overline{BD} \cong \overline{BD}$: Reflexive Property of Congruence
$\angle ABD \cong \angle CBD$: Given (implied, or Angle Bisector Definition if $BD$ bisects $\angle ABC$)
$\triangle ABD \cong \triangle CBD$: ASA (Angle-Side-Angle) Congruence Postulate