To determine whether triangles ΔFGH and ΔIJK are similar, we need to use the definitions of transformations and similarity, which include:
- Proportional Sides: Two triangles are similar if the lengths of their corresponding sides are in proportion.
- Congruent Angles: Two triangles are similar if their corresponding angles are congruent.
In this case, without specific lengths or angle measures provided, we would typically assess the options given based on the information that might lead us to conclude similarity.
Among the options provided:
- "Yes. All sides are proportional." indicates that the ratios of the lengths of the corresponding sides are equal.
- "Yes. All angles are congruent." indicates that the corresponding angles in both triangles are equal.
If at least one of these conditions is satisfied (proportional sides or congruent angles), we can conclude that the triangles are similar.
If the choices present variations of point J's coordinates altering the relationship between the triangles but don't present a situation where the triangles are confirmed not to be similar based on given proportions or angles, we would lean towards confirming similarity.
In conclusion, based on common criteria for similarity and given that there is mention of all sides being proportional and/or all angles being congruent in the options, the correct assessment would be:
Yes. All sides are proportional. This would confirm similarity provided there is evidence for proportional relationships between the sides of the triangles.
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