Question

1. look at the figure. how can you prove △abd and △acd are congruent? it is not possible to determine if the triangles are congruent. △abd≅△acd by the sss postulate. △abd≅△acd by the sas postulate.

Explanation:

Step1: Identify equal - sides and angles

From the figure, we can see that $AB = AC$ (marked with one dash), $AD$ is common to both $\triangle ABD$ and $\triangle ACD$, and $\angle BAD=\angle CAD$ (marked with arcs).

Step2: Apply congruence postulate

The Side - Angle - Side (SAS) postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. Here, in $\triangle ABD$ and $\triangle ACD$, we have two sides ($AB = AC$ and $AD=AD$) and the included angle between them ($\angle BAD=\angle CAD$).

Answer:

$\triangle ABD\cong\triangle ACD$ by the SAS Postulate.