To determine: Whether the triangle ABC and GHI are similar to each other. Given: Triangle ABC that is 75% of its corresponding side in triangle DEF. Triangle GHI that is 32% of its corresponding side in triangle DEF.

To determine: Whether the triangle ABC and GHI are similar to each other. Given: Triangle ABC that is 75% of its corresponding side in triangle DEF. Triangle GHI that is 32% of its corresponding side in triangle DEF.

Question
Similarity
asked 2021-03-02
To determine: Whether the triangle ABC and GHI are similar to each other.
Given:
Triangle ABC that is 75% of its corresponding side in triangle DEF.
Triangle GHI that is 32% of its corresponding side in triangle DEF.

Answers (1)

2021-03-03
Calculation:
Since, \(\displaystyle\triangle{A}{B}{C}\sim\triangle{D}{E}{F}\) then,
\(\displaystyle\frac{{{A}{B}}}{{{D}{E}}}=\frac{{{B}{C}}}{{{E}{F}}}\)
\(\displaystyle=\frac{{{A}{C}}}{{{D}{F}}}\)
Since, \(\displaystyle\triangle{G}{H}{I}\sim\triangle{D}{E}{F}\) then,
\(\displaystyle\frac{{{G}{H}}}{{{D}{E}}}=\frac{{{H}{I}}}{{{E}{F}}}\)
\(\displaystyle=\frac{{{G}{I}}}{{{D}{F}}}\)
If all sides of the triangle are similar then, its angles are also similar to each other.
Then, the triangles \(\displaystyle\triangle{A}{B}{C}\sim\triangle{G}{H}{I}\) since, the triangle \(\displaystyle\triangle{D}{E}{F}\) is similar in both the triangle by SAS similarity.
Therefore, the triangle ABC and GHI are similar to each other by SAS similarity.
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