Rhombus diagonals create right angles

Consider equal sided parallelogram ABCD with diagonals BD, AC intersecting at O.

∠BAC = ∠BCA               (∆ABC isos. AB=CA)

∠DAC = ∠DCA               (∆ADC isos. AD=CD)

∠BAC = ∠DCA               (alt. ang.s  AB || DC)

So ∠BAC = ∠BCA = ∠DAC = ∠DCA