Question

Show that each diagonal of a rhombus bisects the angle through which it passes :

Answer 1

In rhombus ABCD, AC is its diagonal we have to prove that AC bisects $\angle A$ and $\angle C$.

A Now, in $\Delta ABC$ and $\Delta ADC$
AC = AC (Common)
AB = CD (Sides of a rhombus)
BC=AD
$\therefore \Delta ABC\cong \Delta ADC$ (SSS condition)
$\therefore \angle BAC=\angle DACand\angle BCA=\angle DCA$ (c.p.c.t.)
Hence AC bisects the angle A.
Similarly, by joining BD, we can prove that BD bisects $\angle B$ and $\angle D$.

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