如图,AC⊥AB,BD⊥AB,AD和BC相交于E,EF⊥AB.求证:∠AFC=∠BFDsorry,没图,有相同的题帮忙打上去啦!

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如图,AC⊥AB,BD⊥AB,AD和BC相交于E,EF⊥AB.求证:∠AFC=∠BFDsorry,没图,有相同的题帮忙打上去啦!
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如图,AC⊥AB,BD⊥AB,AD和BC相交于E,EF⊥AB.求证:∠AFC=∠BFDsorry,没图,有相同的题帮忙打上去啦!
如图,AC⊥AB,BD⊥AB,AD和BC相交于E,EF⊥AB.求证:∠AFC=∠BFD
sorry,没图,有相同的题帮忙打上去啦!

如图,AC⊥AB,BD⊥AB,AD和BC相交于E,EF⊥AB.求证:∠AFC=∠BFDsorry,没图,有相同的题帮忙打上去啦!
证明:
∵AC⊥AB,BD⊥AB,EF⊥AB
∴AC//FE//BD
∴⊿BFE∽⊿BAC=>EF/AC=BF/AB=>EF×AB=AC×BF
   ⊿AFE∽⊿ABD=>EF/BD=AF/AB=>EF×AB=BD×AF
∴AC×BF=BD×AF=>AC/BD=AF/BF
又∵∠CAF=∠DBF=90º
∴⊿CAF∽⊿DBF【对应边成比例夹角相等】
∴∠AFC=∠BFD