Question

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

Explanation:

Step1: Recall Similar Triangles Property

For similar triangles \( \triangle RST \sim \triangle RYX \) (by SSS similarity), corresponding sides are proportional. So, the ratios of corresponding sides are equal. The corresponding sides are: \( RS \) corresponds to \( RY \), \( RT \) corresponds to \( RX \), and \( ST \) corresponds to \( YX \).

Step2: Identify Corresponding Sides Ratio

We know \( \frac{RT}{RX} \) and \( \frac{RS}{RY} \) are ratios of corresponding sides. The ratio of the third pair of corresponding sides \( ST \) (from \( \triangle RST \)) and \( YX \) (from \( \triangle RYX \)) should also be equal. So, \( \frac{ST}{YX} \) is equal to \( \frac{RT}{RX} \) and \( \frac{RS}{RY} \).

Answer:

\(\frac{ST}{YX}\) (corresponding to the option with \(\frac{ST}{YX}\))