1. The problem involves comparing three triangles: \(\triangle ABC\), \(\triangle DEF\), and \(\triangle GHI\) with given side lengths.
2. We want to determine which triangle is similar to \(\triangle ABC\) by checking if the ratios of corresponding sides are equal.
3. The sides of \(\triangle ABC\) are 6, 7, and 7.
4. For \(\triangle DEF\), the sides are 0.7, 0.7, and 0.6.
5. For \(\triangle GHI\), the sides are 3, 3.5, and 3.5.
6. Calculate the ratios of sides of \(\triangle DEF\) to \(\triangle ABC\):
$$\frac{0.7}{6} = 0.1167, \quad \frac{0.7}{7} = 0.1, \quad \frac{0.6}{7} = 0.0857$$
These are not equal, so \(\triangle DEF\) is not similar to \(\triangle ABC\).
7. Calculate the ratios of sides of \(\triangle GHI\) to \(\triangle ABC\):
$$\frac{3}{6} = 0.5, \quad \frac{3.5}{7} = 0.5, \quad \frac{3.5}{7} = 0.5$$
All ratios are equal, so \(\triangle GHI\) is similar to \(\triangle ABC\).
8. Therefore, the correct answer is \(\triangle GHI\).
Triangle Similarity 690Dab
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