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 (SSS similarity), corresponding sides are proportional. So, in \( \triangle RST \sim \triangle RYX \), the order of the letters gives corresponding sides: \( RS \) corresponds to \( RY \), \( RT \) corresponds to \( RX \), and \( ST \) corresponds to \( YX \).

Step2: Identify Proportional Ratios

Since corresponding sides are proportional, \( \frac{RS}{RY} = \frac{RT}{RX} = \frac{ST}{YX} \). We check each option:

• Option 1: \( \frac{XY}{TS} \) – Inverse and wrong correspondence.
• Option 2: \( \frac{SY}{RY} \) – \( SY \) is not a corresponding side.
• Option 3: \( \frac{RX}{XT} \) – \( XT \) is not a corresponding side.
• Option 4: \( \frac{ST}{YX} \) – Matches the proportionality of corresponding sides.

Answer:

D. \(\frac{ST}{YX}\) (assuming D is the option for \(\frac{ST}{YX}\); if options are labeled as given, the correct one is the last option: \(\frac{ST}{YX}\))