Question

prove that \\( \triangle stv \cong \triangle suv \\).

Explanation:

Step1: Identify the given angles

We are given that \(\angle T=\angle U\) (marked in the diagram) and \(\angle TSV = \angle USV\) (marked in the diagram).

Step2: Identify the common side

\(SV = SV\) (common side for both \(\triangle STV\) and \(\triangle SUV\)).

Step3: Apply the AAS (Angle - Angle - Side) congruence criterion

In \(\triangle STV\) and \(\triangle SUV\), we have two pairs of equal angles (\(\angle T=\angle U\) and \(\angle TSV=\angle USV\)) and a non - included side (\(SV\)) that is equal. By the AAS (Angle - Angle - Side) congruence criterion, \(\triangle STV\cong\triangle SUV\).

Answer:

\(\triangle STV\cong\triangle SUV\) by the AAS (Angle - Angle - Side) congruence criterion.