To determine which ratio is also equal to both [tex]\(\frac{RT}{RX}\)[/tex] and [tex]\(\frac{RS}{RY}\)[/tex], let's analyze the given ratios and see how they simplify. We need to identify one of the given options that matches the structure of [tex]\(\frac{RT}{RX}\)[/tex] and [tex]\(\frac{RS}{RY}\)[/tex].
Given ratios for comparison:
1. [tex]\(\frac{RT}{RX}\)[/tex]
2. [tex]\(\frac{RS}{RY}\)[/tex]
Let's analyze each option provided:
1. [tex]\(\frac{XY}{TS}\)[/tex]
- This ratio involves parts [tex]\(XY\)[/tex] and [tex]\(TS\)[/tex]. There is no immediate simplification to compare with [tex]\(\frac{RT}{RX}\)[/tex] and [tex]\(\frac{RS}{RY}\)[/tex].
2. [tex]\(\frac{SY}{RY}\)[/tex]
- Simplifying [tex]\(\frac{SY}{RY}\)[/tex] can lead to [tex]\(\frac{S}{R}\)[/tex], which is not equivalent to the ratios we're comparing.
3. [tex]\(\frac{RX}{XT}\)[/tex]
- We should look carefully at this.
- Simplifying [tex]\(\frac{RX}{XT}\)[/tex], if these terms are proportional, it can match the given structure.
4. [tex]\(\frac{ST}{YX}\)[/tex]
- This ratio involves [tex]\(ST\)[/tex] and [tex]\(YX\)[/tex]. There is no direct proportional simplification that matches the given ratios.
Upon careful consideration of the options, we can see that:
- [tex]\(\frac{RT}{RX}\)[/tex] and [tex]\(\frac{RS}{RY}\)[/tex] hold a similar structural form.
- The ratio that fits this structural analogy from the options provided is [tex]\(\frac{RX}{XT}\)[/tex].
Thus, the correct ratio that matches both [tex]\(\frac{RT}{RX}\)[/tex] and [tex]\(\frac{RS}{RY}\)[/tex] is [tex]\(\frac{RX}{XT}\)[/tex].
So, the ratio [tex]\(\frac{RX}{XT}\)[/tex] is also equal to [tex]\(\frac{RT}{RX}\)[/tex] and [tex]\(\frac{RS}{RY}\)[/tex].
Therefore, the correct option is:
[tex]\[
\boxed{3}
\][/tex]
