Side Splitter Proportion 1Dcc7C

1. **State the problem:** We are given a proportion based on the side-splitter theorem: $$\frac{JM}{MK} = \frac{LN}{?}$$ and we need to find which side length completes the proportion.\n\n2. **Recall the side-splitter theorem:** It states that if a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally.\n\n3. **Identify the segments:** The proportion compares segments on two sides of the triangle. The left side is $$\frac{JM}{MK}$$, so the right side must be a ratio of segments on the other side cut by the parallel line.\n\n4. **Match the segments:** The segments corresponding to $$JM$$ and $$MK$$ are $$LN$$ and the segment adjacent to $$LN$$ on the same side. The missing segment is the one adjacent to $$LN$$, which is $$NM$$.\n\n5. **Complete the proportion:** $$\frac{JM}{MK} = \frac{LN}{NM}$$\n\n**Final answer:** The side length that completes the proportion is **NM**.