Step 1

The figure of the triangles are given by

Step 2

From the figure we can write as

\(\displaystyle{\frac{{{G}{H}}}{{{J}{L}}}}={\frac{{{45}}}{{{15}}}}={3}\)...(1)

\(\displaystyle{\frac{{{H}{I}}}{{{L}{K}}}}={\frac{{{36}}}{{{12}}}}={3}\)...(2)

\(\displaystyle{\frac{{{G}{I}}}{{{J}{K}}}}={\frac{{{75}}}{{{25}}}}={3}\)...(3)

From equations (1), (2) and (3) we get,

\(\displaystyle{\frac{{{G}{H}}}{{{J}{L}}}}={\frac{{{H}{I}}}{{{L}{K}}}}={\frac{{{G}{I}}}{{{J}{K}}}}\)...(3)

Relation (3) states that all the three corresponding sides of the triangles are proportional.

So, the triangles \(\displaystyle\triangle{G}{H}{I}\sim\triangle{J}{L}{K}\) by SSS similarity.

The figure of the triangles are given by

Step 2

From the figure we can write as

\(\displaystyle{\frac{{{G}{H}}}{{{J}{L}}}}={\frac{{{45}}}{{{15}}}}={3}\)...(1)

\(\displaystyle{\frac{{{H}{I}}}{{{L}{K}}}}={\frac{{{36}}}{{{12}}}}={3}\)...(2)

\(\displaystyle{\frac{{{G}{I}}}{{{J}{K}}}}={\frac{{{75}}}{{{25}}}}={3}\)...(3)

From equations (1), (2) and (3) we get,

\(\displaystyle{\frac{{{G}{H}}}{{{J}{L}}}}={\frac{{{H}{I}}}{{{L}{K}}}}={\frac{{{G}{I}}}{{{J}{K}}}}\)...(3)

Relation (3) states that all the three corresponding sides of the triangles are proportional.

So, the triangles \(\displaystyle\triangle{G}{H}{I}\sim\triangle{J}{L}{K}\) by SSS similarity.