Question

1. look at the figure. how can you prove \\( \triangle abd \\) and \\( \triangle acd \\) are congruent?

it is not possible to determine if the triangles are congruent
\\( \triangle abd \cong \triangle acd \\) by the sas postulate.
\\( \triangle abd \cong \triangle acd \\) by the sss postulate.

Explanation:

Step1: Identify the corresponding sides and angles

From the figure, we can see that \(AB = AC\) (marked with the same tick), \(\angle BAD=\angle CAD\) (marked with the same arc), and \(AD = AD\) (common side).

Step2: Apply the 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.
In \(\triangle ABD\) and \(\triangle ACD\), we have \(AB = AC\), \(\angle BAD=\angle CAD\), and \(AD = AD\). So, we can use the SAS postulate.

Answer:

\(\triangle ABD\cong\triangle ACD\) by the SAS Postulate.