Question

consider △rst and △ryx. if the triangles are similar, which must be true? options: \\(\frac{ry}{rs} = \frac{rx}{rt} = \frac{xy}{ts}\\), \\(\frac{ry}{rx} = \frac{rs}{rt} = \frac{xy}{ts}\\), \\(\frac{ry}{rs} = \frac{rx}{rt} = \frac{rs}{ry}\\), \\(\frac{ry}{ys} = \frac{rx}{xt} = \frac{xy}{ts}\\)

Explanation:

Step1: Recall Similar Triangles Property

For similar triangles, corresponding sides are proportional. In $\triangle RST$ and $\triangle RYX$, the common angle is $\angle R$ (by reflexive property). So, the corresponding sides should be: $RY$ corresponds to $RS$, $RX$ corresponds to $RT$, and $XY$ corresponds to $TS$.

Step2: Check Proportionality

The ratio of corresponding sides should be equal. So, $\frac{RY}{RS}=\frac{RX}{RT}=\frac{XY}{TS}$, which matches the first option.

Answer:

$\boldsymbol{\frac{RY}{RS} = \frac{RX}{RT} = \frac{XY}{TS}}$ (the first option)