Question

1. △adb≅△cdb by the

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

Explanation:

In triangles $\triangle ADB$ and $\triangle CDB$, $\angle ADB=\angle CDB = 90^{\circ}$ (right - angles), $\angle A=\angle C$ (given by the equal - angle markings), and $BD = BD$ (common side). By the Angle - Angle - Side (AAS) Theorem, which 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, the two triangles are congruent.

Answer:

A. AAS Theorem