Question
Show that each diagonal of a rhombus bisects the angle through which it passes.
✓
Answer
In $\triangle\text{AED}$ and $\triangle\text{DEC}$:
$\text{AE}=\text{EC}$ (diagonals bisect each other)
$\text{AD}=\text{DC}$ (sides are equal)
$\text{DE}=\text{DE}$ (common)
By SSS congruence:
$\triangle\text{AED}\cong\triangle\text{CED}$
$\angle\text{ADE}=\angle\text{CDE}$ (c.p.c.t)
Similarly,
we can prove $\triangle\text{AEB}$ and $\triangle\text{BEC}$,
$\triangle\text{BEC}$ and $\triangle\text{DEC}$,
$\triangle\text{AED}$ and $\triangle\text{AEB}$ are congruent to each other.
Hence, diagonal of a rhombus bisects the angle through which it passes.
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