Question

consider \\( \triangle rst \\) and \\( \triangle ryx \\).
if the triangles are similar, which must be true?
\\( \frac { r y } { y s } = \frac { r x } { x t } = \frac { x y } { t s } \\)
\\( \frac { r y } { r s } = \frac { r x } { r t } = \frac { x y } { t s } \\)
\\( \frac { r y } { r s } = \frac { r x } { r t } = \frac { r s } { r y } \\)
\\( \frac { r y } { r x } = \frac { r s } { r t } = \frac { x y } { t s } \\)

Explanation:

Step1: Recall the property of similar triangles

If two triangles \(\triangle RST\) and \(\triangle RYX\) are similar, then the ratios of their corresponding sides are equal.

Step2: Identify the corresponding sides

In \(\triangle RST\) and \(\triangle RYX\), \(RY\) corresponds to \(RS\), \(RX\) corresponds to \(RT\), and \(XY\) corresponds to \(TS\).
So, \(\frac{RY}{RS}=\frac{RX}{RT}=\frac{XY}{TS}\)

Answer:

\(\frac{RY}{RS}=\frac{RX}{RT}=\frac{XY}{TS}\) (the second option)