## nikki156789 3 years ago 15. Calculate NL. a. 30 b. 48 c. 64 d. 72 16. Calculate MN. a. 37.5 b. 80 c. 90 d. 54

1. SUROJ

what is NL?

2. nikki156789

|dw:1332477081850:dw|

3. nikki156789

how would i go about finding these lengths if i dont have the equation to do so?

4. SUROJ

You should use the concept of Similar triangle......the sides of similar triangle are proportional

5. nikki156789

okso since it has two similar sides where would i go from there?

6. nikki156789

hello?

7. SUROJ

did you find all the three angles of two triangles are same

8. nikki156789

no?

9. nikki156789

besides the given ones and l

10. SUROJ

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

11. nikki156789

ok so can you help me find nl?

12. nikki156789

im like super bad at math...as you can tell

13. SUROJ

so see (NL/24)=(24/9)

14. SUROJ

and you can find NL

15. nikki156789

so its 24 divided by 9? or is it a fraction?

16. SUROJ

No, its (24*24/9).....did you catch it?

17. nikki156789

or do i cross multiply? oh wait i get it now

18. SUROJ

yea you cross multiply

19. nikki156789

ok so what do i do for 16?

20. SUROJ

which16?

21. nikki156789

number 16

22. SUROJ

is there any 16 anywhere?

23. nikki156789

yes it says calculate MN

24. Directrix

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.