if the dagonal of a quadilateral bisect the opposite angle,then it isa-------?

If diagonal of a quadrilateral bisect the opposite angles, then it is a rhombus.

ABCD is a rhombus.

∴ AB = BC =  CD = AD

In ΔABC and ΔADC, we have

AB = AD

BC = CD

CA = CA  (Common)

∴ ΔABC ΔADC  (SSS congruence criterion)

⇒ ∠BAC = ∠DAC    (CPCT)

and ∠ACB = ∠ACD  (CPCT)

⇒ AC bisects ∠A and ∠C.

Similarly, it can be proved that BD bisects ∠B and ∠D.