Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Get expert answers to your questions quickly and accurately from our dedicated community of professionals. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
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 appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.