I'll give you the game plan . . . you fill in the details.
We know that: .AB = CD, AD = BC .(Opposite sides of a parallelogram are equal)Prove: If a diagonal of a parallelogram bisects an angle of the parallelogram,
the parallelogram is a rhombus.
We need to show that two adjacent sides are equal: say, AB = BC.
We know that: .angle A = angle C. .(Opposite angles of a parallelogram are equal)
AC bisects angles A and C.
. . Hence: /1 = /2 = /3
Since /2 = /3, triangle ABC is isosceles.
Therefore: .AB = BC