SOLUTION: prove parallelogram ABCD is a rhombus(question) given: AC bisects angles BAD and BCD given: ABCD is a parallelogram

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To prove the parallelogram is a rhombus you have to show that AB = BC = CD = DA.
To prove AB = DA and BC = CD, we need to prove triangles ABC and ADC are congruent.
Because angle BAC = angle DAC, angle BCA = angle DCA, and AC = AC, so triangles ABC and ADC are congruent.
Hence AB = DA and BC = CD.
Next we need to show that AB = CD, this is obvious because they are the opposite sides of a parallelogram.
So AB = BC = CD = DA