Question

△rst ~ △ryx by the sss similarity theorem. which ratio is also equal to \\(\frac{rt}{rx}\\) and \\(\frac{rs}{ry}\\)? options: \\(\frac{xy}{ts}\\), \\(\frac{sy}{ry}\\), \\(\frac{rx}{xt}\\), \\(\frac{st}{yx}\\)

Explanation:

Step1: Recall SSS Similarity

For similar triangles \( \triangle RST \sim \triangle RYX \) (SSS similarity), corresponding sides are proportional. So, \( \frac{RS}{RY} = \frac{RT}{RX} = \frac{ST}{YX} \).

Step2: Match the Ratio

We need to find a ratio equal to \( \frac{RT}{RX} \) and \( \frac{RS}{RY} \). From the similarity, the ratio of corresponding sides \( ST \) (from \( \triangle RST \)) and \( YX \) (from \( \triangle RYX \)) should be equal. So, \( \frac{ST}{YX} \) is the required ratio.

Answer:

\( \boldsymbol{\frac{ST}{YX}} \) (the last option: \( \frac{ST}{YX} \))