Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Join our Q&A platform to connect with experts dedicated to providing precise answers to your questions in different areas. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
We can check each option.
a) We have to prove that x = 8.
The sides KN and MN should have the same length, so we can write:
[tex]\begin{gathered} KN=MN \\ 7x-4=5x+12 \\ 7x-5x=12+4 \\ 2x=16 \\ x=\frac{16}{2} \\ x=8 \end{gathered}[/tex]As x has to be 8, this option is true.
b) This option states that KN = 24.
We can test this using the value of x we have just calculated:
[tex]\begin{gathered} KN=7x-4 \\ KN=7\cdot8-4 \\ KN=56-4 \\ KN=52 \end{gathered}[/tex]This option is false, as KN = 52.
c) As MN = KN, and KN = 52 (from the last calculation), we can conclude that MN = 52.
Then, this option is true.
d) This option states that KL ≅ ML.
By symmetry, the two sides have to have the same length and are congruent, so this option is true.
e) This option states that LM ≅ LN.
This two segments can not be equal, as they are part of a right angle and the hypotenuse as LN can not have the same length as a leg, like LM.
This option is false.
Answer: the true options are A, C and D.
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.