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

For similar triangles, the ratios of corresponding sides are equal.

Step2: Identify corresponding sides

In $\triangle RYX$ and $\triangle RST$, $RY$ corresponds to $RS$, $RX$ corresponds to $RT$, and $XY$ corresponds to $TS$.

Step3: Write the ratio of corresponding sides

So, by the property of similar triangles, we have $\frac{RY}{RS}=\frac{RX}{RT}=\frac{XY}{TS}$.

Answer:

$\frac{RY}{RS}=\frac{RX}{RT}=\frac{XY}{TS}$