# 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,

###### Question:

## Answers

C) HF is 4 units and GH is 2 units.

Step-by-step explanation:

The SSS similarity theorem says that if the side-lengths of the corresponding sides of two triangles are proportional then the triangles are similar.

In ΔDFE and ΔGFH ,

DG = 15, GF = 5, EH = 12, and DE = 8.

To prove ΔDFE and ΔGFH are similar by using SSS similarity theorem we need :-

[tex]\frac{DF}{GF}=\frac{FE}{FH}=\frac{DE}{GH}\\\\\Rightarrow\frac{DG+GF}{GF}=\frac{FH+EH}{FH}=\frac{DE}{GH}\\\\\Rightarrow\frac{5+15}{5}=\frac{12+HF}{FH}=\frac{8}{GH}\\\\\Rightarrow\frac{20}{5}=\frac{12+HF}{FH}\ and\ \frac{20}{5}=\frac{8}{GH}\\\\\Rightarrrow4HF=12+HF\ and\ GH=\frac{8}{4}\\\\\Rightarrow3HF=12\ and\ GH=2\\\\\Rightarrow HF=4\ and\ GH=2[/tex]

Hence, To prove that △DFE ~ △GFH by the SSS similarity theorem using the information provided in the diagram, it would be enough additional information to know that HF is 4 units and GH is 2 units.

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Step-by-step explanation:

answer is C

Step-by-step explanation:

B

Step-by-step explanation:

I JUST TOOK THE QUIZ

I believe the answer would be B because it makes the most sense putting the figures scaled in my head with the already designated lengths

I think its C: SAS Similarity;9

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

LM is 5 units and xz is 6 units

Step-by-step explanation:

LM corresponds to XY

mn to yz and nl to zx

The answer is B; the triangle is 4x larger than the smaller one.

SSS stands for side-side-side.

It is a criterion for triangles' similarity.

This criterion tells that if the 3 sides of two triangles have same ratio, then the two triangles are similar.

In this case, you have to refer to the figure to check that if HF is 4 units and GH is 2 units, you can infere that the SSS crieterion is satisfied.

For example, you will find these ratios 8/10 = 4/5.

Then, the answer is the option C. HF is 4 units and GH is 2 units.