Show that each diagonal of a rhombus

In $\triangle \mathrm{AED}$ and $\Delta \mathrm{DEC}:$

$\mathrm{AE}=\mathrm{EC}$ (diagonals bisect each other)

$\mathrm{AD}=\mathrm{DC}$ (sides are equal)

$\mathrm{DE}=\mathrm{DE}$ (common)

$\mathrm{By} \mathrm{SSS}$ congruence :

$\triangle \mathrm{AED} \cong \Delta \mathrm{CED}$

$\angle \mathrm{ADE}=\angle \mathrm{CDE}$ (c. p.c.t)

Similarly, we can prove $\Delta \mathrm{AEB}$ and $\Delta \mathrm{BEC}, \Delta \mathrm{BEC}$ and $\Delta \mathrm{DEC}, \Delta \mathrm{AED}$ and $\Delta \mathrm{AEB}$ are congruent to each other.

Hence, diagonal of a rhombus bisects the angle through which it passes.