Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
Given that [tex]\(\triangle HLI \sim \triangle JLK\)[/tex] by the SSS (Side-Side-Side) similarity theorem, we know that the corresponding sides of similar triangles are proportional.
In this situation, let's denote the sides of [tex]\(\triangle HLI\)[/tex] and [tex]\(\triangle JLK\)[/tex] as follows:
- [tex]\(\triangle HLI\)[/tex] has sides [tex]\(H-L\)[/tex], [tex]\(L-I\)[/tex], and [tex]\(H-I\)[/tex].
- [tex]\(\triangle JLK\)[/tex] has sides [tex]\(J-L\)[/tex], [tex]\(L-K\)[/tex], and [tex]\(J-K\)[/tex].
Since the triangles are similar by the SSS similarity theorem, the ratios of their corresponding sides are equal. Therefore, we can write the following ratio relationships:
[tex]\[ \frac{HL}{JL} = \frac{IL}{KL} = \frac{HI}{JK} \][/tex]
Now let's check the given options to determine which one matches the equal ratio [tex]\( \frac{HL}{JL} = \frac{IL}{KL} \)[/tex]:
- [tex]\(\frac{HI}{JK}\)[/tex]
Here, [tex]\( \frac{HI}{JK} \)[/tex] matches the ratio of corresponding sides.
Therefore, the ratio that is equal to [tex]\(\frac{HL}{JL} = \frac{IL}{KL}\)[/tex] is:
[tex]\[ \frac{HI}{JK} \][/tex]
Thus, the correct answer is that [tex]\(\frac{HL}{JL} = \frac{IL}{KL}\)[/tex] is also equal to [tex]\(\frac{HI}{JK}\)[/tex].
[tex]\[ \boxed{3} \][/tex]
In this situation, let's denote the sides of [tex]\(\triangle HLI\)[/tex] and [tex]\(\triangle JLK\)[/tex] as follows:
- [tex]\(\triangle HLI\)[/tex] has sides [tex]\(H-L\)[/tex], [tex]\(L-I\)[/tex], and [tex]\(H-I\)[/tex].
- [tex]\(\triangle JLK\)[/tex] has sides [tex]\(J-L\)[/tex], [tex]\(L-K\)[/tex], and [tex]\(J-K\)[/tex].
Since the triangles are similar by the SSS similarity theorem, the ratios of their corresponding sides are equal. Therefore, we can write the following ratio relationships:
[tex]\[ \frac{HL}{JL} = \frac{IL}{KL} = \frac{HI}{JK} \][/tex]
Now let's check the given options to determine which one matches the equal ratio [tex]\( \frac{HL}{JL} = \frac{IL}{KL} \)[/tex]:
- [tex]\(\frac{HI}{JK}\)[/tex]
Here, [tex]\( \frac{HI}{JK} \)[/tex] matches the ratio of corresponding sides.
Therefore, the ratio that is equal to [tex]\(\frac{HL}{JL} = \frac{IL}{KL}\)[/tex] is:
[tex]\[ \frac{HI}{JK} \][/tex]
Thus, the correct answer is that [tex]\(\frac{HL}{JL} = \frac{IL}{KL}\)[/tex] is also equal to [tex]\(\frac{HI}{JK}\)[/tex].
[tex]\[ \boxed{3} \][/tex]
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.