如图所示,AC⊥AB,BD⊥AB,AD与BC相交于E,求证1/S△ABC+1/S△ABD=1/S△ABC

Question

如图所示,AC⊥AB,BD⊥AB,AD与BC相交于E,求证1/S△ABC+1/S△ABD=1/S△ABC

Answer 1

【纠正：求证1/S△ABC+1/S△ABD=1/S△ABE】证明：作EF⊥AB于F∵AC⊥AB,BD⊥AB∴AC//EF//BD∴⊿BEF∽⊿BAC,＝＞EF/AC=BF/AB ⊿AEF∽⊿ADB,＝＞EF/BD=AF/AB两等式左加左等于右加右EF/AC+EF/BD=(BF+AF )/AB=AB/AB=1EF/A...