Answer :
If [tex]\(\triangle RST\)[/tex] is similar to [tex]\(\triangle RYX\)[/tex] by the SSS (Side-Side-Side) similarity theorem, all corresponding sides of these similar triangles will have equal ratios.
Given:
[tex]\[ \frac{RT}{RX} = \frac{RS}{RY} \][/tex]
Since triangles are similar, the corresponding sides are proportional. The same ratio must apply to the third set of corresponding sides, which are [tex]\(ST\)[/tex] in [tex]\(\triangle RST\)[/tex] and [tex]\(XY\)[/tex] in [tex]\(\triangle RYX\)[/tex].
Thus, the ratio [tex]\(\frac{ST}{XY}\)[/tex] must also be equal to [tex]\(\frac{RT}{RX}\)[/tex] and [tex]\(\frac{RS}{RY}\)[/tex].
Therefore, the ratio that is also equal to [tex]\(\frac{RT}{RX}\)[/tex] and [tex]\(\frac{RS}{RY}\)[/tex] is:
[tex]\[ \frac{ST}{XY} \][/tex]
So, the correct answer is:
[tex]\[\boxed{\frac{S T}{X Y}}\][/tex]
Given:
[tex]\[ \frac{RT}{RX} = \frac{RS}{RY} \][/tex]
Since triangles are similar, the corresponding sides are proportional. The same ratio must apply to the third set of corresponding sides, which are [tex]\(ST\)[/tex] in [tex]\(\triangle RST\)[/tex] and [tex]\(XY\)[/tex] in [tex]\(\triangle RYX\)[/tex].
Thus, the ratio [tex]\(\frac{ST}{XY}\)[/tex] must also be equal to [tex]\(\frac{RT}{RX}\)[/tex] and [tex]\(\frac{RS}{RY}\)[/tex].
Therefore, the ratio that is also equal to [tex]\(\frac{RT}{RX}\)[/tex] and [tex]\(\frac{RS}{RY}\)[/tex] is:
[tex]\[ \frac{ST}{XY} \][/tex]
So, the correct answer is:
[tex]\[\boxed{\frac{S T}{X Y}}\][/tex]
