Determine (if possible) the similarity postulate that proves the following two triangles are similar:

Step 1
Given two triangles are :

Step 2
${\displaystyle \mathrm{△}GHI}$,
GH=42, HI=17, IG=48
${\displaystyle \mathrm{△}LMN}$,
LM=21, MN=10, NL=30
Step 3
We know that if two triangles are similar then their sides are in equal ratio.
if ${\displaystyle \mathrm{△}GHI\text{and}\mathrm{△}LMN}$ are similar then,
${\displaystyle \frac{GH}{LM}=\frac{HI}{MN}=\frac{GI}{LN}}$
Here,
${\displaystyle \frac{GH}{LM}=\frac{42}{21}=2}$
${\displaystyle \frac{HI}{MN}=\frac{17}{10}=1.7}$
${\displaystyle \frac{GI}{LN}=\frac{48}{30}=1.6}$,
That means, ${\displaystyle \frac{GH}{LM}\ne q\frac{HI}{MN}\ne q\frac{GI}{LN}}$
Hence given two triangles are not similar, ${\displaystyle \mathrm{△}GHIn\sim \mathrm{△}LMN}$
Answer : These triangles are not similar.