Question

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

Answer 1

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.