Final answer:
The correct answer to the problem is option d. EF/LM = EG/LN, because in similar triangles, corresponding sides are proportional to each other. The ratio of any pair of corresponding sides for triangles EFG and LMN is 3:1, confirming the proportionality.
Step-by-step explanation:
The student has asked if triangles △ EFG and △ LMN are similar with a ratio of 3:1, which of the following statements is true:
- a. EG≡ LM
- b. EF≡ LM
- c. EG/LN = FG/MN
- d. EF/LM = EG/LM
Firstly, for similar triangles, corresponding sides are in the same ratio. So the sides of △ EFG would be three times the corresponding sides of △ LMN.
Now let's analyze the given options:
Option a can't be correct because EG can't be congruent to LM if the triangles are similar in a ratio of 3:1.
Option b is also incorrect for the same reason as option a.
For option c, EG/LN being equal to FG/MN could be possible if EG corresponds to LM and FG corresponds to MN, but we are looking for a ratio involving both triangles, and EG and FG are from the same triangle.
Option d is the correct option because if we have EF/LM for one pair of corresponding sides, this should equal the ratio for any other pair of corresponding sides, such as EG/LN or FG/MN, since the triangles are similar. The question mentions the ratio is 3:1, which confirms that the ratio of any pair of corresponding sides will also be 3:1.
Therefore, we mention the correct option answer in the final answer: d. EF/LM = EG/LN.