ABCD là hình thang => AB // CD
=> $\widehat{ABD}= \widehat{BDC}$ (so le trong)
Ta có:
$\frac{AB}{BD}= \frac{9}{12}= \frac{3}{4}$
$\frac{BD}{DC}= \frac{12}{16}= \frac{3}{4}$
=> $\frac{AB}{BD}= \frac{BD}{DC}$
$\Delta$ ABD và $\Delta$ BDC có:
$\frac{BD}{DC}= \frac{AB}{BD}$
$\widehat{ABD}= \widehat{BDC}$
=> $\Delta$ ABD $\sim$ $\Delta$ BDC (c.g.c)