# 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.
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Theodore Schwartz
Calculation:
Since, $\mathrm{△}ABC\sim \mathrm{△}DEF$ then,
$\frac{AB}{DE}=\frac{BC}{EF}$
$=\frac{AC}{DF}$
Since, $\mathrm{△}GHI\sim \mathrm{△}DEF$ then,
$\frac{GH}{DE}=\frac{HI}{EF}$
$=\frac{GI}{DF}$
If all sides of the triangle are similar then, its angles are also similar to each other.
Then, the triangles $\mathrm{△}ABC\sim \mathrm{△}GHI$ since, the triangle $\mathrm{△}DEF$ is similar in both the triangle by SAS similarity.
Therefore, the triangle ABC and GHI are similar to each other by SAS similarity.