Question

1. what additional information do you need to prove \\( \triangle abc=\triangle def \\) by the sas postulate?

\\( \angle cab=\angle fde \\)
\\( \angle bca=\angle efd \\)
\\( \angle abc=\angle def \\)

Explanation:

Step1: Recall SAS Postulate

SAS (Side - Angle - Side) 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 \(\triangle ABC\) and \(\triangle DEF\), we already have \(AC = DF\) (marked with one tick) and \(BC=EF\) (marked with two ticks).

Step2: Identify the included angle

The included angle for sides \(AC\) and \(BC\) in \(\triangle ABC\) is \(\angle BCA\), and the included angle for sides \(DF\) and \(EF\) in \(\triangle DEF\) is \(\angle EFD\).

Answer:

\(\angle BCA\cong\angle EFD\) (the second option)