Question

∆ADB ≅ ∆CDB by the _____

Answer 1

The marked angles and side BD make up two adjacent angles and a side not between them. The applicable theorem is ...
   AAS Theorem

Answer 2

Answer:

Option A is correct

AAS theorem.

Step-by-step explanation:

AAS(Angle -Angle-Side) theorem states that:

if two angles and any side of one triangle are congruent to two angles and any side of another triangle, then these triangles are congruent

In a given triangle ADB and CDB.

$\angle BAD = \angle BCD$  [Angle]                      [Given]

$\angle BDA = \angle BDC=90^{\circ}$  [Angle]        [Given]

$BD = BD$   {Common side}       [Side]

then by AAS theorem;

$\triangle ADB \cong \triangle CDB$

Therefore, ∆ADB ≅ ∆CDB by the AAS theorem.