1. **State the problem:** We have two triangles, ONM and KML, with NO parallel to KL. Given lengths are KL = 21, NO = 14, ML = 24, and KM = 15. We need to find the length of NM. 2. **Use the properties of similar triangles:** Since NO is parallel to KL, triangles ONM and KML are similar by the AA (Angle-Angle) similarity criterion. 3. **Set up the ratio of corresponding sides:** The ratio of sides in similar triangles is equal. So, $$\frac{NO}{KL} = \frac{NM}{ML} = \frac{OM}{KM}$$ 4. **Plug in known values:** $$\frac{14}{21} = \frac{NM}{24}$$ 5. **Simplify the fraction:** $$\frac{14}{21} = \frac{\cancel{14} \times 1}{\cancel{14} \times 1.5} = \frac{2}{3}$$ 6. **Solve for NM:** $$\frac{2}{3} = \frac{NM}{24} \Rightarrow NM = \frac{2}{3} \times 24$$ 7. **Calculate NM:** $$NM = 16$$ **Final answer:** $$NM = 16$$