如图,已知AB/AD=BC/DE=AC/AE,求证:△ABD∽△ACE.

问题描述:

如图,已知

AB
AD
=
BC
DE
=
AC
AE
,求证:△ABD∽△ACE.

证明:∵

AB
AD
=
BC
DE
=
AC
AE

∴△ABC∽△ADE,
∴∠BAC=∠DAE,
∴∠BAC-∠DAC=∠DAE-∠DAC,
即∠BAD=∠CAE,
AB
AD
=
AC
AE

∴△ABD∽△ACE.