Question

如图,已知锐角△ABC中,BF、CF分别是高线,在在高BE上截取BM=AC,在搞CF延长线上截取CN=AB,连AM、AN

Answer 1

先证 △AMB ≌△NAC.

理由是：

AB = NC

BM = AC

∠ABM = ∠NAC (等角的余角相等)

得AM = AN

2)

因为∠AMB = ∠NAC = 180 - ∠AME = 180 - (90 - ∠CAM)= 90 +∠ CAM

所以∠NAM = ∠NAC - ∠CAM = 90