If ΔEFG ~ ΔLMN with a ratio of 4:1, this means that the corresponding sides of the triangles are in the same ratio.
The correct choice is:
segment EF over segment LM equals segment FG over segment LN
This indicates the proportionality between the corresponding sides of the similar triangles. Thus, \( \frac{EF}{LM} = \frac{FG}{LN} \).
The other options are incorrect because:
- Segment EF is not congruent to segment LM (they are in a ratio of 4:1).
- Segment FG is compared with segment MN, which is not expressed correctly in the options.
- Segment EG cannot be congruent to segment LM since they are corresponding sides in different triangles with different lengths.
So, the most accurate statement regarding the ratio is the first choice about proportionality.