Question

name the theorem or postulate that lets you immediately conclude △abd ≅ △cbd. a aas b sas c sss d asa

Explanation:

Step1: Identify the given information

We have two right - angled triangles \(\triangle ABD\) and \(\triangle CBD\). \(\angle ABD=\angle CBD = 90^{\circ}\), \(\angle A=\angle C\) (given in the figure as angles at \(A\) and \(C\)), and \(BD = BD\) (common side).

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

The AAS (Angle - Angle - Side) congruence criterion states that if two angles and a non - included side of one triangle are equal 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 (\(\angle A=\angle C\) and \(\angle ABD=\angle CBD\)) and a non - included side (\(BD\)) that are equal.

Answer:

A. AAS