# Determine whether the two triangles are similar \triangle GHI\sim \triangle. If they are, complete the similarity statement.

Determine whether the two triangles are similar. If they are, complete the similarity statement.
Select all that apply.
$$\displaystyle\triangle{G}{H}{I}\sim\triangle$$ ? by

The triangles are not similar.
$$\displaystyle\triangle{G}{H}{I}\sim\triangle{K}{L}{J}$$
$$\displaystyle\triangle{G}{H}{I}\sim\triangle{J}{L}{K}$$
By SAS similarity
By SSS similarity
By AA similarity

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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.