To determine if the triangles \( \Delta FGH \) and \( \Delta IJK \) are similar, we can use the definitions of transformations. Triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional.
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If all angles are congruent: This is one of the criteria for similarity. If you can show that all corresponding angles in \( \Delta FGH \) and \( \Delta IJK \) are equal, then the triangles are similar.
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If all sides are proportional: This is another criterion for similarity. If the ratios of the lengths of corresponding sides are equal, then the triangles are similar.
The responses provided suggest considerations of various points for triangle \( IJK \). However, without specific coordinate values or a way to calculate side lengths and angles, we cannot definitively work through these options.
Given the options, let's analyze:
- "Yes. All sides are proportional." If true, then \( \Delta FGH \sim \Delta IJK \) would be valid.
- "Yes. All angles are congruent." This is also a valid condition for similarity.
The responses suggesting spatial changes for point \( J \) indicate that there might be specific conditions under which they could be similar, but without seeing the actual coordinates or a diagram, we can't conclude.
Overall, the strongest conditions for similarity based on the definitions are:
- If you could confirm that either all angles are congruent or all sides are proportional, then the answer would be "Yes."
If you have data showing either of those conditions being met, choose that response. Without more information, it's best to select:
"Yes. All angles are congruent."
Or
"Yes. All sides are proportional."
if you can validate one of those conditions for similarity based on the triangle measurements.
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