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# 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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