Question

1. name the postulate or theorem you can use to prove ( \triangle abdcong\triangle cbd ). sss postulate sas postulate asa postulate aas theorem

Explanation:

Step1: Identify the given information

We know that \(\angle ABD=\angle CBD = 90^{\circ}\) (right angles), \(BD = BD\) (common side), and \(\angle ADB=\angle CDB\) (given equal angles).

Step2: Recall the AAS (Angle - Angle - Side) theorem

The AAS 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.
In \(\triangle ABD\) and \(\triangle CBD\), we have two angles (\(\angle ABD=\angle CBD\) and \(\angle ADB=\angle CDB\)) and a non - included side (\(BD\)) that are congruent.

Answer:

AAS Theorem