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nikki156789

15. Calculate NL. a. 30 b. 48 c. 64 d. 72 16. Calculate MN. a. 37.5 b. 80 c. 90 d. 54

  • 2 years ago
  • 2 years ago

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  1. SUROJ
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    what is NL?

    • 2 years ago
  2. nikki156789
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    |dw:1332477081850:dw|

    • 2 years ago
  3. nikki156789
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    how would i go about finding these lengths if i dont have the equation to do so?

    • 2 years ago
  4. SUROJ
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    You should use the concept of Similar triangle......the sides of similar triangle are proportional

    • 2 years ago
  5. nikki156789
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    okso since it has two similar sides where would i go from there?

    • 2 years ago
  6. nikki156789
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    hello?

    • 2 years ago
  7. SUROJ
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    did you find all the three angles of two triangles are same

    • 2 years ago
  8. nikki156789
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    no?

    • 2 years ago
  9. nikki156789
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    besides the given ones and l

    • 2 years ago
  10. SUROJ
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    one is given initially, the other one are vertically opposite angles and since sum of all angles of triangle are 180 degree, the third angle is also equal

    • 2 years ago
  11. nikki156789
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    ok so can you help me find nl?

    • 2 years ago
  12. nikki156789
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    im like super bad at math...as you can tell

    • 2 years ago
  13. SUROJ
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    so see (NL/24)=(24/9)

    • 2 years ago
  14. SUROJ
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    and you can find NL

    • 2 years ago
  15. nikki156789
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    so its 24 divided by 9? or is it a fraction?

    • 2 years ago
  16. SUROJ
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    No, its (24*24/9).....did you catch it?

    • 2 years ago
  17. nikki156789
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    or do i cross multiply? oh wait i get it now

    • 2 years ago
  18. SUROJ
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    yea you cross multiply

    • 2 years ago
  19. nikki156789
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    ok so what do i do for 16?

    • 2 years ago
  20. SUROJ
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    which16?

    • 2 years ago
  21. nikki156789
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    number 16

    • 2 years ago
  22. SUROJ
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    is there any 16 anywhere?

    • 2 years ago
  23. nikki156789
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    yes it says calculate MN

    • 2 years ago
  24. Directrix
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    First, establish that the two triangles are similar. < J is congruent to <N as marked. <KLJ is congruent to <NLM because vertical angles are congruent. Two pairs of congruent angles is ALL you need to prove triangles similar. A third pair is unnecessary because of the theorem: If two angles of one triangle are congruent to two angles of another triangle, the third pair of angles are also congruent. That is why the AA Triangle Similarity Postulate has ONLY two As in it. Second, establish the correspondence of vertices of the two similar triangles. I got Triangle JKL ~ Triangle NML because J<-->N from the marked congruent angles and L <--> L because of the congruent vertical angles. Those correspondences force K <-- >M. Lengths of corresponding sides of similar triangles are in proportion. Looking at the triangle correspondence Triangle JKL ~ Triangle NML, the extended proportion is as follows: JK/NM = KL/ML = JL/NL. That equation comes directly from the triangle correspondence. JK was first and second in the line-up for Triangle JKL so it corresponds to NM, first and second in the line-up for Triangle NML. Then, I chose second and third to second and third, and finally 3rd and lst to 3rd and lst. Notice that I have not looked at the given lengths of any triangle sides because without the information above, I would not know how to set up the equations. JK/NM = KL/ML = JL/NL My next step is to fill in the known values in this extended proportion. 30 / (NM) = 9 / 24 = 24 / NL Select two fractions where you know 3 of the four quantities. 30 / (NM) = 9 / 24 9 (MN) = 30* 24 MN = (30* 24) / 9 MN = 80 ---> Option B --------------- 9 / 24 = 24 / NL 9 (NL) = 24*24 NL = (24*24) / 9 NL = 64 --> Option C Note: When you work triangle similarity problems, it is *critical* to get the correspondence of the vertices FIRST. That gives you the corresponding sides in a proportion through which you can find the sides you seek. Do check my work to ensure that I correctly read the side lengths.

    • 2 years ago
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