Question

complete the proportion: \\( \frac { r t } { r s } = \frac { v t } { x } \\).
\\( \triangle r s t \sim \triangle v u t \\)
\\( \bigcirc v u \\)
\\( \bigcirc u t \\)
\\( \bigcirc s t \\)
\\( \bigcirc r u \\)

Explanation:

Step1: Use similarity of triangles property

For similar triangles \(\triangle RST\sim\triangle VUT\), the ratios of corresponding sides are equal.
In a proportion \(\frac{RT}{RS}=\frac{VT}{x}\), we need to find the corresponding side to \(RS\).

Step2: Identify corresponding sides

In similar triangles \(\triangle RST\) and \(\triangle VUT\), side \(RS\) in \(\triangle RST\) corresponds to side \(VU\) in \(\triangle VUT\) (by the order of the similarity statement \(\triangle RST\sim\triangle VUT\), which means \(R\) corresponds to \(V\), \(S\) corresponds to \(U\), and \(T\) corresponds to \(T\)).

Answer:

\(VU\)