Question

Prove that a diagonal of a rhombus bisect two opposite angles.

Answer 1

Consider $△$ABC and $△$ADC
AB = AD (All sides of a rhombus are equal.)
AC = AC (Common)
CD = CB (All sides of a rhombus are equal.)
By SSS congruency, $△$ABC $\cong$ $△$ADC.
And,
$\angle$DCA = $\angle$BCA (by c.a.c.t)
$\angle$DAC = $\angle$BAC (by c.a.c.t)
Hence, the diagonal of a rhombus bisects two opposite angles.