In Fig. 17.29, BDEF and DCEF are each a parallelogram.

In parallelogram BDEF

$\therefore \mathrm{BD}=\mathrm{EF} \quad \ldots$ (i) (opposite sides of a parallelogram are equal)

In parallelogram DCEF

$\mathrm{CD}=\mathrm{EF} \quad \ldots$ (ii) $\quad$ (opposite sides of a parallelogram are equal)

From equations (i) and (ii)

$\mathrm{BD}=\mathrm{CD}$