Consider the two triangles. 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.

The corresponding sides are
LN to XZ
LM to XY
NM to ZY

We have NM=3 and ZY=9
The scale factor is 9÷3=3

XZ = 2×3 = 6 units
LM = 12÷3 = 4 units

The correct answer is LM is 4 units and XZ is 6 units

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psm22415 psm22415 · Answer 2 · 2022-02-08T04:29:53+01:00

The correct option is B which is ''LM is 4 units and XZ is 6 units''.

Consider the two triangles. To prove that △LMN ~ △XYZ.

What is the SSS similarity theorem?

The SSS similarity theorem states that when sides of any two triangles are in proportion, this means that these two triangles are similar.

Here; 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.

Since ΔLMN is a smaller triangle by values given, we need to multiply the value of side LN by 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 the ratio of 3:1,

Therefore;

YZ:MN = 3:1

XZ:LN = 3:1

XY:LM = 3:1

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

ΔXYZ:ΔLMN = 3:1

and also

△LMN ~ △XYZ

Hence, the correct option is B which is ''LM is 4 units and XZ is 6 units''.

To know more about SSS postulates theorem click the link given below.

https://brainly.com/question/21247688