Consider the two triangles.

triangles l m n and x y z are shown. side l m is blank, side m n is 3, and side n l is 2. side x y is 12, side y z is 9, and side z x is blank.

to prove that △lmn ~ △xyz by the sss similarity theorem using the information provided in the diagram, it would be enough additional information to know that

lm is 3 units and xz is 5 units.
lm is 4 units and xz is 6 units.
lm is 5 units and xz is 3 units.
lm is 6 units and xz is 4 units.

LM is 4 units and XZ is 6 units.

Step-by-step explanation:

Now, first we have to understand that what is SSS similarity theorem. This theorem states that when sides of any two triangles are in proportion, this means that these two triangles are similar.

By the data given,

we can see that,

YZ:MN = 3:1

So, there is an assumption that ΔXYZ:ΔLMN = 3:1

Now when XY = 12, we need value of LM = 12/3 =4

So, XY: LM would become 3:1

If value of LN is given as 2, we need value of XZ = (2)*(3) = 6

Note that since ΔLMN is smaller triangle by values given, so we need to multiply value of side LN with 3 to get the value of XZ in ratio 3:1

So, by the data given in option 2, we would have all lines of both triangles in ratio of 3:1,

so,

YZ:MN = 3:1

XZ:LN = 3:1

XY:LM = 3:1

Hence, by using SSS postulate for similarity of triangles we would prove that

ΔXYZ:ΔLMN = 3:1

and also

△LMN ~ △XYZ

r = 78539458390583095803458309458039485093485 or just 3

step-by-step explanation: