Join the IDNLearn.com community and start finding the answers you need today. Our platform offers reliable and detailed answers, ensuring you have the information you need.
Sagot :
Given that [tex]\(\triangle RST \sim \triangle RYX\)[/tex] by the SSS (Side-Side-Side) similarity theorem, the corresponding sides of similar triangles are proportional. Let's identify the corresponding sides in these similar triangles:
- [tex]\(RT\)[/tex] in [tex]\(\triangle RST\)[/tex] corresponds to [tex]\(RX\)[/tex] in [tex]\(\triangle RYX\)[/tex]
- [tex]\(RS\)[/tex] in [tex]\(\triangle RST\)[/tex] corresponds to [tex]\(RY\)[/tex] in [tex]\(\triangle RYX\)[/tex]
- [tex]\(ST\)[/tex] in [tex]\(\triangle RST\)[/tex] corresponds to [tex]\(YX\)[/tex] in [tex]\(\triangle RYX\)[/tex]
Given this proportionality, we can write the following ratios between corresponding sides:
- [tex]\(\frac{RT}{RX} = \frac{RS}{RY}\)[/tex]
- [tex]\(\frac{RS}{RY} = \frac{ST}{YX}\)[/tex]
Thus, all three ratios [tex]\(\frac{RT}{RX}\)[/tex], [tex]\(\frac{RS}{RY}\)[/tex], and [tex]\(\frac{ST}{YX}\)[/tex] are equal. The question asks which ratio among the given options is also equal to [tex]\(\frac{RT}{RX}\)[/tex] and [tex]\(\frac{RS}{RY}\)[/tex].
From our analysis, we see that the ratio [tex]\(\frac{ST}{YX}\)[/tex] is equal to these ratios because:
[tex]\[ \frac{RT}{RX} = \frac{RS}{RY} = \frac{ST}{YX} \][/tex]
Therefore, the ratio [tex]\(\frac{ST}{YX}\)[/tex] is the one that is also equal to [tex]\(\frac{RT}{RX}\)[/tex] and [tex]\(\frac{RS}{RY}\)[/tex].
Hence, the correct answer is:
[tex]\(\frac{ST}{YX}\)[/tex]
- [tex]\(RT\)[/tex] in [tex]\(\triangle RST\)[/tex] corresponds to [tex]\(RX\)[/tex] in [tex]\(\triangle RYX\)[/tex]
- [tex]\(RS\)[/tex] in [tex]\(\triangle RST\)[/tex] corresponds to [tex]\(RY\)[/tex] in [tex]\(\triangle RYX\)[/tex]
- [tex]\(ST\)[/tex] in [tex]\(\triangle RST\)[/tex] corresponds to [tex]\(YX\)[/tex] in [tex]\(\triangle RYX\)[/tex]
Given this proportionality, we can write the following ratios between corresponding sides:
- [tex]\(\frac{RT}{RX} = \frac{RS}{RY}\)[/tex]
- [tex]\(\frac{RS}{RY} = \frac{ST}{YX}\)[/tex]
Thus, all three ratios [tex]\(\frac{RT}{RX}\)[/tex], [tex]\(\frac{RS}{RY}\)[/tex], and [tex]\(\frac{ST}{YX}\)[/tex] are equal. The question asks which ratio among the given options is also equal to [tex]\(\frac{RT}{RX}\)[/tex] and [tex]\(\frac{RS}{RY}\)[/tex].
From our analysis, we see that the ratio [tex]\(\frac{ST}{YX}\)[/tex] is equal to these ratios because:
[tex]\[ \frac{RT}{RX} = \frac{RS}{RY} = \frac{ST}{YX} \][/tex]
Therefore, the ratio [tex]\(\frac{ST}{YX}\)[/tex] is the one that is also equal to [tex]\(\frac{RT}{RX}\)[/tex] and [tex]\(\frac{RS}{RY}\)[/tex].
Hence, the correct answer is:
[tex]\(\frac{ST}{YX}\)[/tex]
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your questions find answers at IDNLearn.com. Thanks for visiting, and come back for more accurate and reliable solutions.