MN平行BC,即MN//BC
证明:∵ MN//BC
∴AM/AB = MN/BC
AN/AC = MN/BC
∴AM/AB = AN/AC
则AB/AM = AC/ AN
即(AM+BM)/AM=(AN+NC)/AN
1+BM/AM = 1+NC/AN
∴ BM/AM = NC/AN
∴AM/BM = AN/NC
MN平行BC,即MN//BC
证明:∵ MN//BC
∴AM/AB = MN/BC
AN/AC = MN/BC
∴AM/AB = AN/AC
则AB/AM = AC/ AN
即(AM+BM)/AM=(AN+NC)/AN
1+BM/AM = 1+NC/AN
∴ BM/AM = NC/AN
∴AM/BM = AN/NC