Question

如图,△ABC中,AB=AC,CD⊥AB,CD=2,AD=1,四边形BDEF是正方形,求证:△CEF∽△BDC

Answer 1

由条件：AD=1,CD=2,

∴AC=AB=√5,

△BCD中,BD=√5-1,CD=2,

△CEF中,CE=2-（√5-1）=3-√5,EF=√5-1,

∴（√5-1）/（3-√5）=√5+1,

2/（√5-1）=√5+1.

∴△BDC∽△CEF.

证毕.