證明：∵?$△ABC\sim △A'B'C'$?
∴?$∠B=∠B'，$??$\frac {AB}{A'B'}=\frac {BC}{B'C'}=k$?
∵?$AD$?與?$A'D'$?分別是?$△ABC$?和?$△A'B'C'$?中邊?$BC、$??$B'C'$?上的中線
∴?$BC= 2BD，$??$B'C'=2B'D'$?
∵?$\frac {BC}{B'C'}=k$?
∴?$\frac {2BD}{2B'D'}=k$?
∴?$\frac {BD}{B'D'}=k$?
∴?$\frac {AB}{A'B'}=\frac {BD}{B'D'}=k$?
∴?$△ABD∽△A'B'D'$?
∴?$\frac {AB}{A'B'}=\frac {AD}{A'D'}=k$?
