Final answer:
With the given side lengths, the ratios of JK/MN and KL/NP are both 1/3, suggesting proportionality between the sides of triangles JKL and MNP. However, without information about the angles or the third set of sides, we cannot conclude similarity. Hence, the answer cannot be determined.
Step-by-step explanation:
Determining whether triangles JKL and MNP are similar involves comparing their corresponding sides to see if they are proportional. We have JK = 6 units, KL = 4 units, and we know that MN = 18 units, NP = 12 units. By examining the ratios of the corresponding sides, we get: JK/MN = 6/18 = 1/3 and KL/NP = 4/12 = 1/3. Since both ratios are equal, the sides are proportional.
However, we do not have information about the angles of the triangles or the third set of corresponding sides, so we cannot yet determine if the triangles are similar based on SSS (Side-Side-Side) or AA (Angle-Angle) similarity postulates. Therefore, the answer cannot be determined with the given information (a. Cannot be determined).
If all three sets of corresponding sides were known to be proportional, or if we knew two angles were equal, we could identify a similarity postulate or theorem. As it stands, we're lacking that information.