Question

三角形ABC中,角A=90°,AB=AC,四边形BCDE是矩形,BC=2CD,H是AC中点,联接BD,BH,DH.求证:

Answer 1

∵AB=AC,H为AC中点,∴AH/AB=1/2,

∵BC=2CD,∴CD/BC=1/2,

∴AH/AB=CD/BC,

又∠BAH=∠BCD=90°,

∴ΔABH∽ΔCBD.