anonymous
  • anonymous
15. Calculate NL. a. 30 b. 48 c. 64 d. 72 16. Calculate MN. a. 37.5 b. 80 c. 90 d. 54
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
what is NL?
anonymous
  • anonymous
|dw:1332477081850:dw|
anonymous
  • anonymous
how would i go about finding these lengths if i dont have the equation to do so?

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anonymous
  • anonymous
You should use the concept of Similar triangle......the sides of similar triangle are proportional
anonymous
  • anonymous
okso since it has two similar sides where would i go from there?
anonymous
  • anonymous
hello?
anonymous
  • anonymous
did you find all the three angles of two triangles are same
anonymous
  • anonymous
no?
anonymous
  • anonymous
besides the given ones and l
anonymous
  • anonymous
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
anonymous
  • anonymous
ok so can you help me find nl?
anonymous
  • anonymous
im like super bad at math...as you can tell
anonymous
  • anonymous
so see (NL/24)=(24/9)
anonymous
  • anonymous
and you can find NL
anonymous
  • anonymous
so its 24 divided by 9? or is it a fraction?
anonymous
  • anonymous
No, its (24*24/9).....did you catch it?
anonymous
  • anonymous
or do i cross multiply? oh wait i get it now
anonymous
  • anonymous
yea you cross multiply
anonymous
  • anonymous
ok so what do i do for 16?
anonymous
  • anonymous
which16?
anonymous
  • anonymous
number 16
anonymous
  • anonymous
is there any 16 anywhere?
anonymous
  • anonymous
yes it says calculate MN
Directrix
  • Directrix
First, establish that the two triangles are similar. < J is congruent to 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.

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