Question

1. $\triangle adbcong\triangle cdb$ by the

aas theorem.
sss postulate.
sas postulate.
asa postulate.

Explanation:

Step1: Identify equal elements

In $\triangle ADB$ and $\triangle CDB$, $\angle ADB=\angle CDB = 90^{\circ}$ (right - angles), $\angle A=\angle C$ (given by the angle - markings), and $BD = BD$ (common side).

Step2: Recall congruence postulates

The AAS (Angle - Angle - Side) theorem states that if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent. Here, we have two angles ($\angle A=\angle C$ and $\angle ADB=\angle CDB$) and a non - included side ($BD$).

Answer:

A. AAS Theorem