$证明：∵\frac {AD}{AB}=\frac {A'D'}{A'B'}$
$∴\frac {AD}{A'D'}=\frac {AB}{A'B'}$
$∵\frac {CD}{C'D'}=\frac {AC}{A'C'}=\frac {AB}{A'B'}$
$∴\frac {CD}{C'D'}=\frac {AC}{A'C'}=\frac {AD}{A'D'}$
$∴△ADC∽△A'D'C'$
$∴∠A=∠A'$
$∵\frac {AC}{A'C'}=\frac {AB}{A'B'}$
$∴△ABC∽△A'B'C'$
