Final answer:
Centroid N divides each median of triangle JKL into segments with a ratio of 2:1. Thus, segment KN and MN are each 2/3 the length of JN, which are parts of the medians from vertices K and M, respectively.
Step-by-step explanation:
The question is asking to identify the relationship between the lengths of segments in a triangle with a centroid. A centroid in a triangle is the point where the medians of the triangle intersect, and it has a property that it divides each median into two segments with a specific ratio. Specifically, the centroid divides a median into two segments with a ratio of 2:1, where the segment connecting the centroid to the vertex (the longer one) is twice as long as the segment connecting the centroid to the midpoint of the opposite side.
In this problem, N is the centroid of triangle JKL, meaning that KN and MN are part of the medians from the vertices K and M, respectively, to their opposite sides. Therefore, the correct answers are:
- C. KN = 2/3 of JN: This is because KN is 2 parts of the total 3 parts of the median from vertex K.
- B. MN = 2/3 of JN: Similarly, MN is 2 parts of the total 3 parts of the median from vertex M.