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

Lennie Carroll 2021-08-02 Answered
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
image
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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Expert Answer

Clara Reese
Answered 2021-08-03 Author has 15770 answers
Step 1
The figure of the triangles are given by
image
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.
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