Question

如图1-3-13，△ABC中∠C为直角，△DEF中∠F为直角，DE⊥AC，交AC于G，交AB于H，DF⊥AB，交AB于I，求证:△ABC∽△DEF.

图1-3-13

Answer 1

证明：∵HI⊥DF，EF⊥DF,

∴HI∥EF，∠DIH=∠DFE=90°.

∴∠DHI=∠DEF.∴△DHI∽△DEF.

∵∠DIH=∠AGH=90°，∠DHI=∠AHG,∴△DHI∽△AHG.

∵∠A=∠A，∠AGH=∠ACB=90°,

∴△AGH∽△ACB.∴△ABC∽△DE F