Question

ilarity transformations
consider △rst and △ryx.
if the triangles are similar, which must be true?
\\(\frac{ry}{rx} = \frac{rs}{rt} = \frac{xy}{ts}\\)
\\(\frac{ry}{rs} = \frac{rx}{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 $\angle R$. So, the corresponding sides should be: $RY$ corresponds to $RS$, $RX$ corresponds to $RT$, and $XY$ corresponds to $TS$.

Step2: Check Proportionality

So the ratio of corresponding sides should be $\frac{RY}{RS}=\frac{RX}{RT}=\frac{XY}{TS}$.

Answer:

$\frac{RY}{RS} = \frac{RX}{RT} = \frac{XY}{TS}$ (the second option among the given choices, i.e., the one with $\frac{RY}{RS} = \frac{RX}{RT} = \frac{XY}{TS}$)