Question

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

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

AA similarity postulate
SAS similarity postulate
SSS similarity postulate
These triangles are not similar

2021-08-06
Step 1
Given two triangles are :

Step 2
$$\displaystyle\triangle{G}{H}{I}$$,
GH=42, HI=17, IG=48
$$\displaystyle\triangle{L}{M}{N}$$,
LM=21, MN=10, NL=30
Step 3
We know that if two triangles are similar then their sides are in equal ratio.
if $$\displaystyle\triangle{G}{H}{I}\ {\quad\text{and}\quad}\ \triangle{L}{M}{N}$$ are similar then,
$$\displaystyle{\frac{{{G}{H}}}{{{L}{M}}}}={\frac{{{H}{I}}}{{{M}{N}}}}={\frac{{{G}{I}}}{{{L}{N}}}}$$
Here,
$$\displaystyle{\frac{{{G}{H}}}{{{L}{M}}}}={\frac{{{42}}}{{{21}}}}={2}$$
$$\displaystyle{\frac{{{H}{I}}}{{{M}{N}}}}={\frac{{{17}}}{{{10}}}}={1.7}$$
$$\displaystyle{\frac{{{G}{I}}}{{{L}{N}}}}={\frac{{{48}}}{{{30}}}}={1.6}$$,
That means, $$\displaystyle{\frac{{{G}{H}}}{{{L}{M}}}}\ne{q}{\frac{{{H}{I}}}{{{M}{N}}}}\ne{q}{\frac{{{G}{I}}}{{{L}{N}}}}$$
Hence given two triangles are not similar, $$\displaystyle\triangle{G}{H}{I}{n}\sim\triangle{L}{M}{N}$$
Answer : These triangles are not similar.